lim _{x rightarrow 0} frac{(1-e^x) sin x}{x^2 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) We need to evaluate the limit: $\lim _{x \rightarrow 0} \frac{(1-e^x) \sin x}{x^2+x^3}$ Factor out $x^2$ from the denominator: $\lim _{x \rightarr

Vedclass · Accepted Answer

$-1$

Vedclass · Answer

(A) We need to evaluate the limit: $\lim _{x ightarrow 0} \frac{(1-e^x) \sin x}{x^2+x^3}$ Factor out $x^2$ from the denominator: $\lim _{x ightarrow 0} \frac{(1-e^x) \sin x}{x^2(1+x)}$ Rewrite the expression as: $\lim _{x}$ ${ightarrow 0} \left( \frac{1-e^x}{x} ight) 	imes \left( \frac{\sin x}{x} ight) 	imes \left( \frac{1}{1+x} ight)$ Using standard limits $\lim _{x ightarrow 0} \frac{e^x-1}{x} = 1$ and $\lim _{x ightarrow 0} \frac{\sin x}{x} = 1$: The expression becomes: $(-1) 	imes (1) 	imes \left( \frac{1}{1+0} ight) = -1 	imes 1 	imes 1 = -1$

$\lim _{x \rightarrow 0} \frac{(1-e^x) \sin x}{x^2+x^3}$ is equal to

Similar Questions

If $a, b, c$ are non-coplanar unit vectors such that $a \times (b \times c) = \frac{b + c}{\sqrt{2}}$,then what is the angle between $a$ and $b$?

Three identical charges are placed at the vertices of an equilateral triangle. The force experienced by each charge, (if $k=1 / 4 \pi \varepsilon_0$ ) is

If $f(x) = \frac{\cos^2 x + \sin^4 x}{\sin^2 x + \cos^4 x}$, for $x \in R$, then $f(2002)$ is equal to

Which of the following is a bactericidal antibiotic?

The work function of nickel is $5 \text{ eV}$. When light of wavelength $2000 \text{ \AA}$ falls on it, it emits photoelectrons. The potential difference necessary to stop the fastest electrons emitted is (given $h = 6.67 \times 10^{-34} \text{ J-s}$): (in $\text{ V}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module