Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Evaluate  <img alt="\mathrm{\lim _{x \rightarrow 0^{+}}\left(\frac{\cos ^2 x}{x}-\frac{e^x}{\sin x}\right)}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5Clim%20_%7B

Evaluate  \mathrm{\lim _{x \rightarrow 0^{+}}\left(\frac{\cos ^2 x}{x}-\frac{e^x}{\sin x}\right)}

Option: 1

0


Option: 2

-1


Option: 3

1


Option: 4

2


Answers (1)

best_answer

\begin{aligned} \lim _{x \rightarrow 0^{+}}\left(\frac{\cos ^2(x)}{x}-\frac{e^x}{\sin (x)}\right) & =\lim _{x \rightarrow 0^{+}}\left(\frac{\sin (x) \cos ^2(x)-x e^x}{x \sin (x)}\right) \\ \\& =\lim _{x \rightarrow 0^{+}}\left(\frac{\sin (x)(1+\cos (2 x))-2 x e^x}{2 x \sin (x)}\right) \\ \\& =\lim _{x \rightarrow 0^{+}}\left(\frac{\left(x+o\left(x^2\right)\right)(1+1+o(x))-2 x(1+x+o(x))}{2 x(x+o(x))}\right) \end{aligned}

                                                        \begin{aligned} \\& =\lim _{x \rightarrow 0^{+}}\left(\frac{2 x-2 x-2 x^2+o\left(x^2\right)}{2 x^2+o\left(x^2\right)}\right) \\ \\& =\lim _{x \rightarrow 0^{+}}\left(\frac{-2 x^2+o\left(x^2\right)}{2 x^2+o\left(x^2\right)}\right) \\ \\& =\lim _{x \rightarrow 0^{+}}(-1+o(1)) \\ \\& =-1 \end{aligned}

Posted by

Sanket Gandhi

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Mains 2026: AI & Data Science cutoffs show NIT Warangal at top
anam-khan

JEE Mains 2026 cut-offs for new NITs and IIITs: What to expect?
anam-khan

JEE Main Result 2026 LIVE: Session 2 results at jeemain.nta.nic.in soon; toppers, final answer key awaited

Latest Question