Find lim x → 1 ( x − 1 ) ln ( sin − 1 ( ln x ) ) .

Let t = x − 1 . As t → 0 + , ln ( 1 + t ) ∼ t and sin − 1 ( ln ( 1 + t )) ∼ t . Hence the expression is asymptotic to t ln t , which tends to 0.

Start Free Mock LoginAlready registered? Login here

Mathematics - Limits Question with Solution | TestHub

MathematicsLimitsExponential and logarithmic limitsMedium2 minQB

MathematicsMediumsingle choice

Find $lim_{x \to 1} (x - 1) ln (sin^{- 1} (ln x))$ .

Options:

Answer:

Solution:

Let $t = x - 1$ . As $t \to 0^{+}, ln (1 + t) \sim t$ and $sin^{- 1} (ln (1 + t)) \sim t$ . Hence the expression is asymptotic to $t ln t$ , which tends to 0.

Stream:JEESubject:MathematicsTopic:LimitsSubtopic:Exponential and logarithmic limits

⏱ 2mℹ️ Source: QB

Doubts & Discussion

Loading discussions...