Mathematics - Limits Question with Solution | TestHub

Paragraph:Read the following passage and answer the questions. For every function $f(x)$ which is twice differentiable, these will be good approximation of ${\int }_a^{b}f(x)dx\cong \left(\frac{b-a}{2}\right)\{f(a)+f(b)\}$. Now, if we take $c=\frac{a+b}{2}$, then using above again, we get ${\int }_a^{b}f(x)dx={\int }_a^{c}f(x)dx+{\int }_c^{b}f(x)dx\cong \frac{b-a}{4}\{f(a)+f(b)+2f(c)\}$ and so on. We get approximation for value of ${\int }_a^{b}f(x)dx$.Question:If ${\lim }_{t\to a}\frac{{\int }_a^{t}f(x)dx-\frac{(t-a)}{2}\{f(t)+f(a)\}}{(t-a{)}^3}=0$, then degree of polynomial function $f(x)$ at most is