Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2026
Exam
NDA
Year
2026
Subject
Mathematics
Chapter
Limits

NDA 2026 · Mathematics · Limits

What is _ x→0 10^ x -1 x equal to ?

What is lim⁡x→010sin⁡x−1tan⁡x\lim\limits_{x\to0}\dfrac{10^{\sin x}-1}{\tan x} equal to ?

Options

  1. A00
  2. B11
  3. Cln⁡10\ln 10
  4. Dlog⁡10e\log_{10}e

Correct answer

C. ln⁡10\ln 10

Step-by-step solution

The given limit is lim⁡x→010sin⁡x−1tan⁡x\lim_{x\to0}\dfrac{10^{\sin x}-1}{\tan x}

Multiplying and dividing the expression by sin⁡x\sin x:

\lim_{x\to0} \left(\dfrac{10^{\sin x}-1}{\sin x} \times \dfrac{\sin x}{\tan x}\right)<br><br>\lim_{x\to0} \left(\dfrac{10^{\sin x}-1}{\sin x} \times \cosx\right)<br><br>Usingthestandardlimit<br><br>Using the standard limit\lim_{t\to0}\dfrac{a^t-1}{t} = \ln a, where t=sin⁡x→0t = \sin x \to 0 as x→0x \to 0:

ln⁡10×cos⁡0\ln 10 \times \cos 0

ln⁡10×1=ln⁡10\ln 10 \times 1 = \ln 10

Answer: $\ln 10
Practice Limits on Quantrex Academy →

More from Limits

What is _ x→1 x^ (n^2-1) -1 x^ (n+1) -1 equal to, where n > 1 is a natural number ? NDA 2026Consider the following for the two (02) items that follow: Let the function f(x) = x^2 +… NDA 2025For the following three (03) items: Consider the function f(x) = x|x| . What is _ x → -1… NDA 2025For the following two (02) items: Let f(x) = cases (1 - 2x)/(x^2), & x 0 cases What is _… NDA 2025For the following two (02) items: Let f(x) = cases (1 - 2x)/(x^2), & x 0 cases What is _… NDA 2025Consider the following for the two (02) items that follow: Let the function f(x) = [x]… NDA 2025Consider the following for the two (02) items that follow: Let the function f(x) = [x]… NDA 2025Consider the following for the two (02) items that follow: Let the function f(x) = x^2… NDA 2025What is ( θ- θ) equal to? x arrow (π)/(2) NDA 2024Which one of the following is correct regarding _ x arrow 3 (|x-3|)/(x-3) ? NDA 2024Let f(x)=|x|+1 and g(x)=[x]-1 , where [.] is the greatest integer function. Let… NDA 2024Let f(x) a^ x-1 b^ x-1 and g(x)=x-1 . What is _ x arrow 1 (f(x)-1)/(g(x)) equal to? NDA 2023Let f(x)=|x| and g(x)=[x]-1 , where [.] is the greatest integer function. Let… NDA 2023Let f(x) a^ x-1 b^ x-1 and g(x)=x-1 . What is _ x arrow 1 f(x)^ (1)/(g(x)) equal to? NDA 2023What is _ x arrow 1 (x^9-1)/(x^3-1) equal to? NDA 2023Let f(x)=\ array cc a x(x+1)+b, & x < 1 x-1 & 1 ≤ x ≤ 2 array . What is _ x arrow 0 f(x)… NDA 2023 Full Limits list Limits JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs