Mathematics › Continuity - Differentiability
Continuity - Differentiability Questions
246 questions across 4 subtopics — with step-by-step solutions.
Continuity- IMVT(5)
- Let be a real differentiable function such... | Mathematics | TestHub
- If the functionis continuous at , then is... | Mathematics | TestHub
- Let denote the greatest integer function,... | Mathematics | TestHub
- Let be continuous at . Then is equal to | Mathematics | TestHub
- If \mathrm{f}(\mathrm{x}) is twice differe... | Mathematics | TestHub
Continuity- Miscellaneous(93)
- Let f(x) = \lim_{n \to \infty} \frac{x^{2n... | Mathematics | TestHub
- Let f: \mathbb{R} \to \mathbb{R} be a func... | Mathematics | TestHub
- Let f: \mathbb{R} \to \mathbb{R} be a func... | Mathematics | TestHub
- Let f(x) = \begin{cases} \frac{1-\cos(kx)}... | Mathematics | TestHub
- Let f: \mathbb{R} \to \mathbb{R} be a func... | Mathematics | TestHub
- Let f(x) = \lim_{n \to \infty} \frac{x^n \... | Mathematics | TestHub
- Let f: \mathbb{R} \to \mathbb{R} be a func... | Mathematics | TestHub
- Let f: \mathbb{R} \to \mathbb{R} be a cont... | Mathematics | TestHub
- Let be a function defined on the interval... | Mathematics | TestHub
- Let be a continuous function defined by .... | Mathematics | TestHub
- The value of and for which the function is... | Mathematics | TestHub
- If is a function defined by , where denote... | Mathematics | TestHub
- Let be a function satisfying , for all and... | Mathematics | TestHub
- For every integer , let and be real number... | Mathematics | TestHub
- Let then is | Mathematics | TestHub
- Statement 1: A function is continuous at i... | Mathematics | TestHub
- Consider the function : where is the great... | Mathematics | TestHub
- Let , and ; then the set of all points whe... | Mathematics | TestHub
- Let be a composite function of defined by... | Mathematics | TestHub
- Let If is continuous at | Mathematics | TestHub
- If the functionis continuous at, thenequals | Mathematics | TestHub
- Letbe a continuous function and letbe defi... | Mathematics | TestHub
- Letbe a non - zero real number. Ifis a con... | Mathematics | TestHub
- If a function is given by , then at | Mathematics | TestHub
- Let be a function such that If is differen... | Mathematics | TestHub
- LetIf the function, defined as,is continuo... | Mathematics | TestHub
- The number of points at which the function... | Mathematics | TestHub
- The value of, so that the functionis conti... | Mathematics | TestHub
- Letbe the greatest integer less than or eq... | Mathematics | TestHub
- The value ofwhich the functionis continuou... | Mathematics | TestHub
- If the functiondefined asis continuous at,... | Mathematics | TestHub
- Let The value of for which is continuous a... | Mathematics | TestHub
- Letthenis continuous but not differentiabl... | Mathematics | TestHub
- Letbe a function defined asThenis: | Mathematics | TestHub
- If the functiondefined onbyis continuous,... | Mathematics | TestHub
- Letbe defined asWheredenotes the greatest... | Mathematics | TestHub
- If the functionis continuous atthen the va... | Mathematics | TestHub
- Ifis continuous at, then the ordered pairi... | Mathematics | TestHub
- Letforwheredenotes the greatest integer fu... | Mathematics | TestHub
- Ifis continuous at, thenis equal to: | Mathematics | TestHub
- If the functiondefined onby, is continuous... | Mathematics | TestHub
- Letdenote the greatest integerandThen the... | Mathematics | TestHub
- If a function defined by be continuous for... | Mathematics | TestHub
- Let be the function defined by | Mathematics | TestHub
- If the function is continuous at then is e... | Mathematics | TestHub
- Let be defined as, If is continuous at the... | Mathematics | TestHub
- Letdenote the greatest integer less than o... | Mathematics | TestHub
- If the functionis continuous at each point... | Mathematics | TestHub
- Letbe such that the functionis continuous... | Mathematics | TestHub
- Let . Defined a function, If is continuous... | Mathematics | TestHub
- Letandbe defined asand, whereare non-negat... | Mathematics | TestHub
- Let be defined as If is continuous on , th... | Mathematics | TestHub
- Let be a function defined asIf is continuo... | Mathematics | TestHub
- Let a function be defined as, Where is the... | Mathematics | TestHub
- Letdenote the greatest integerThe number o... | Mathematics | TestHub
- Let be defined aswhere is the greatest int... | Mathematics | TestHub
- Let be defined as If is continuous at then... | Mathematics | TestHub
- Consider the function, andwhereis a polyno... | Mathematics | TestHub
- Ifis a function defined bywheredenotes the... | Mathematics | TestHub
- Letbe defined aswhereanddenotes greatest i... | Mathematics | TestHub
- Let the function be continuous at . Then i... | Mathematics | TestHub
- The functiondefined byis continuous for allin | Mathematics | TestHub
- Letand, whereis the greatest integer. Then... | Mathematics | TestHub
- The number of points where the function, w... | Mathematics | TestHub
- If the functionis continuous at, thenis eq... | Mathematics | TestHub
- Ifandare continuous on, thenis equal to: | Mathematics | TestHub
- Letbe functions defined byandwheredenote t... | Mathematics | TestHub
- If for, then functionis continuous at, then | Mathematics | TestHub
- If the function is continuous at , then is... | Mathematics | TestHub
- Let be the greatest integer . Then the num... | Mathematics | TestHub
- Let, whereanddenotes the greatest integer... | Mathematics | TestHub
- Letbe the function defined as, wheredenote... | Mathematics | TestHub
- Let be a function given by where . If is c... | Mathematics | TestHub
- Let be a function given by where . If is c... | Mathematics | TestHub
- For , let be a continous function at . The... | Mathematics | TestHub
- Let be given by , where denotes the greate... | Mathematics | TestHub
- Consider the function ,wheredenotes the gr... | Mathematics | TestHub
- If the function is continuous at , then th... | Mathematics | TestHub
- Let be the function defined by | Mathematics | TestHub
- If the function , is continuous at , then... | Mathematics | TestHub
- Let denote the greatest integer less than... | Mathematics | TestHub
- If the function is continuous at , then is... | Mathematics | TestHub
- Let be continuous at . Then is equal to | Mathematics | TestHub
- The number of points of discontinuity of t... | Mathematics | TestHub
- A function f(x) is defined by , f(x)=\left... | Mathematics | TestHub
- If the function f defined by f(x)=\frac{\l... | Mathematics | TestHub
- Let f(x)=\left\{\begin{array}{ll}\frac{x^{... | Mathematics | TestHub
- If the function f defined by f(x)=\frac{x(... | Mathematics | TestHub
- The function f(x)=\frac{1}{u^{2}-u-2} wher... | Mathematics | TestHub
- Let \mathrm{f}(\mathrm{x})=\left[\mathrm{x... | Mathematics | TestHub
- Let \mathrm{f}(\mathrm{x})=\left\{\begin{a... | Mathematics | TestHub
- The number of two digits numbers ' a ' who... | Mathematics | TestHub
- Which is discontinuous at x=1 | Mathematics | TestHub
Differentiability(134)
- Let N be the total number of points in the... | Mathematics | TestHub
- Match the functions in Column I with their... | Mathematics | TestHub
- Let f: \mathbb{R} \to \mathbb{R} be a func... | Mathematics | TestHub
- Let S be the set of all values of K for wh... | Mathematics | TestHub
- Let f: \mathbb{R} \to \mathbb{R} be a func... | Mathematics | TestHub
- Let f(x) = x^2 |x-c| e^{ax} be a function.... | Mathematics | TestHub
- Let f: \mathbb{R} \to \mathbb{R} be a func... | Mathematics | TestHub
- Let f(x) = (x^2-9) |x-3| . The number of p... | Mathematics | TestHub
- Let f: \mathbb{R} \to \mathbb{R} be a func... | Mathematics | TestHub
- Let f: \mathbb{R} \to \mathbb{R} be a func... | Mathematics | TestHub
- Let f: \mathbb{R} \to \mathbb{R} be a func... | Mathematics | TestHub
- Let f(x) = \min(x^2, \alpha x + \beta) . I... | Mathematics | TestHub
- If | Mathematics | TestHub
- The set of points where is differentiable is | Mathematics | TestHub
- If , then | Mathematics | TestHub
- Let be a function defined by . Then which... | Mathematics | TestHub
- In the following denotes the greatest inte... | Mathematics | TestHub
- Let . Then which one of the following is t... | Mathematics | TestHub
- Let and be real valued functions defined o... | Mathematics | TestHub
- Let and . Statement-1 : gof is differentia... | Mathematics | TestHub
- Let be a real-valued function defined on t... | Mathematics | TestHub
- The value of is | Mathematics | TestHub
- Let for , and . If is continuous at , then... | Mathematics | TestHub
- Let be a function such that . If is differ... | Mathematics | TestHub
- If , then | Mathematics | TestHub
- If , then as a function of , at is | Mathematics | TestHub
- If , where , is differentiable at , then | Mathematics | TestHub
- Consider the function . Statement : Statem... | Mathematics | TestHub
- Letbe a function such thatfor allThen, atis | Mathematics | TestHub
- Letandbe respectively given byandDefinebyT... | Mathematics | TestHub
- Let and . Then | Mathematics | TestHub
- Let Then which one of the following is true? | Mathematics | TestHub
- Let be two functions defined by and Statem... | Mathematics | TestHub
- If the functionis differentiable, then the... | Mathematics | TestHub
- Letbe a differentiable function withandLet... | Mathematics | TestHub
- If then is | Mathematics | TestHub
- Letandbe defined by. Thenis - | Mathematics | TestHub
- If the functionis differentiable at, theni... | Mathematics | TestHub
- Letandbe functions defined byand, whereden... | Mathematics | TestHub
- Forand, then | Mathematics | TestHub
- Consider the greatest integer function, de... | Mathematics | TestHub
- If, then | Mathematics | TestHub
- Letis a differential function}. Then,is a... | Mathematics | TestHub
- Letandbe functions defined by(i)(ii), wher... | Mathematics | TestHub
- Let , , is a differentiable function . The... | Mathematics | TestHub
- LetThen, the setis equal to: | Mathematics | TestHub
- Letwhere the functionsatisfiesfor all natu... | Mathematics | TestHub
- Let be the set of all real values of where... | Mathematics | TestHub
- LetLetbe the set of points in the interval... | Mathematics | TestHub
- Letbe a differentiable function fromtosuch... | Mathematics | TestHub
- Letbe a function defined byIfbe the set of... | Mathematics | TestHub
- Let and Then, in the interval is: | Mathematics | TestHub
- Letbe differentiable atand. If, then atis: | Mathematics | TestHub
- LetThen the set of all values of, at which... | Mathematics | TestHub
- Letbe the set of all points inat which the... | Mathematics | TestHub
- Let the functions and be defined by , wher... | Mathematics | TestHub
- Letbe the set of points where the function... | Mathematics | TestHub
- Let, be the set of all functions, which ar... | Mathematics | TestHub
- Let the functionbe defined byand letbe an... | Mathematics | TestHub
- Let be a differentiable function such that... | Mathematics | TestHub
- If the functionis twice differentiable, th... | Mathematics | TestHub
- Letbe defined as. The value offor whichexi... | Mathematics | TestHub
- The functionis : | Mathematics | TestHub
- Let and be functions satisfying for all If... | Mathematics | TestHub
- Letbe a function defined by.Letdenote the... | Mathematics | TestHub
- Letbe any function defined onand let it sa... | Mathematics | TestHub
- then the number of points in the interval... | Mathematics | TestHub
- then the number of points in the interval... | Mathematics | TestHub
- Let the functions and be defined as : and... | Mathematics | TestHub
- The functionis not differentiable at exact... | Mathematics | TestHub
- Letsatisfy the equationfor allandfor any.... | Mathematics | TestHub
- Let a function be defined asthen the numbe... | Mathematics | TestHub
- Let be a function defined as Let be given... | Mathematics | TestHub
- Ifis differentiable at every point of the... | Mathematics | TestHub
- Letbe defined bywhereis the greatest integ... | Mathematics | TestHub
- Let be defined as where is the greatest in... | Mathematics | TestHub
- The number of points, at which the functio... | Mathematics | TestHub
- Ifthen | Mathematics | TestHub
- A function is defined on aswhere denotes t... | Mathematics | TestHub
- Letbe a function defined by. Then which of... | Mathematics | TestHub
- Let .ConsiderThen, | Mathematics | TestHub
- The number of points, where the function,... | Mathematics | TestHub
- Let, wheredenotes the greatest integer les... | Mathematics | TestHub
- Ifdenotes the greatest integer, then numbe... | Mathematics | TestHub
- be two real valued function defined asand,... | Mathematics | TestHub
- Letbe a function defined by :Whereis the g... | Mathematics | TestHub
- Let a function be defined as:where . If is... | Mathematics | TestHub
- Let. Ifis the number of points, whereis no... | Mathematics | TestHub
- Letwheredenotes greatest integer. Ifis the... | Mathematics | TestHub
- Suppose f is a function satisfyingfor alla... | Mathematics | TestHub
- Letdenote the greatest integer function an... | Mathematics | TestHub
- Letandbe the greatest integer, then the nu... | Mathematics | TestHub
- Letbe defined bywheredenotes the greatest... | Mathematics | TestHub
- Letandbe two functions defined byand.Thenis | Mathematics | TestHub
- Letandbe positive real numbers such that t... | Mathematics | TestHub
- Let and be twice differentiable functions... | Mathematics | TestHub
- Let, then at | Mathematics | TestHub
- Consider the function defined by . If and... | Mathematics | TestHub
- If the functionis differentiable on, theni... | Mathematics | TestHub
- Let be defined asIf is continuous everywhe... | Mathematics | TestHub
- Consider the functiondefined byand the fun... | Mathematics | TestHub
- Letbe differentiable inand. Then the value... | Mathematics | TestHub
- If is the number of points where is not di... | Mathematics | TestHub
- Letandbe real constants such that the func... | Mathematics | TestHub
- Let. Ifanddenote the number of points wher... | Mathematics | TestHub
- Letbe a function satisfyingfor all. If, then | Mathematics | TestHub
- Let be a linear function and , is continuo... | Mathematics | TestHub
- Let and be the number of points at which t... | Mathematics | TestHub
- Let the function be not differentiable at... | Mathematics | TestHub
- Let the function, be differentiable for al... | Mathematics | TestHub
- Let where [.] denotes greatest integer fun... | Mathematics | TestHub
- Let denote the greatest integer function,... | Mathematics | TestHub
- Let be a real differentiable function such... | Mathematics | TestHub
- Number of values of x in [-4,4] where f(x)... | Mathematics | TestHub
- Suppose ' f ' is a function that satisfies... | Mathematics | TestHub
- Which of the following functions are not d... | Mathematics | TestHub
- If a Î (-¥,-1) È (-1,0) then the number of... | Mathematics | TestHub
- If \mathrm{f}(\mathrm{x})=\mathrm{a}\left|... | Mathematics | TestHub
- Let a function f: R \rightarrow R satisfie... | Mathematics | TestHub
- Consider the function f(x)=x^{2}+b x+c , w... | Mathematics | TestHub
- Let f:(-\infty, \infty) \rightarrow[0, \in... | Mathematics | TestHub
- If f\left(\frac{x+y}{2}\right)=\frac{f(x)+... | Mathematics | TestHub
- Let a function f: R \rightarrow R satisfie... | Mathematics | TestHub
- Let \mathrm{f}(\mathrm{x})=\left\{\begin{a... | Mathematics | TestHub
- The function \mathrm{f}(\mathrm{x})=\left|... | Mathematics | TestHub
- A function f: R \rightarrow R where R is a... | Mathematics | TestHub
- A function f: R \rightarrow R satisfies th... | Mathematics | TestHub
- If \mathrm{f}(\mathrm{x})=\left\{\begin{ar... | Mathematics | TestHub
- If f(x)= maximum \left\{4,1+x^{2}, x^{2}-1... | Mathematics | TestHub
- Let \varnothing\left(\frac{x+2 y}{3}\right... | Mathematics | TestHub
- The function \mathrm{f}(\mathrm{x})=\left(... | Mathematics | TestHub
- If the function is differentiable at , then: | Mathematics | TestHub
- Let f(x)=x^{2} \sin \frac{1}{x} for 0<x \l... | Mathematics | TestHub
- Let and are integers, and let be the left... | Mathematics | TestHub
Miscellaneous/Mixed(14)
- Let f: \mathbb{R} \to \mathbb{R} be a func... | Mathematics | TestHub
- Let f(x) = \begin{cases} x^a \sin\left(\fr... | Mathematics | TestHub
- Let f(x) = \begin{cases} x^2+ax+b & , x \l... | Mathematics | TestHub
- Let f: \mathbb{R} \to \mathbb{R} be a diff... | Mathematics | TestHub
- Match the functions in Column I with their... | Mathematics | TestHub
- Let f: \mathbb{R} \to \mathbb{R} be a diff... | Mathematics | TestHub
- If , then at is | Mathematics | TestHub
- Let f(x) be a real function not identicall... | Mathematics | TestHub
- The function is | Mathematics | TestHub
- Which of the following is the only correct... | Mathematics | TestHub
- Consider the function ' \phi ' defined in... | Mathematics | TestHub
- Which of the following is the only correct... | Mathematics | TestHub
- Which of the following is the only correct... | Mathematics | TestHub
- Let f be a continuous function and satisfi... | Mathematics | TestHub
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