Q: Evaluate $\lim{x \to 0} \frac{\sin x}{x}$.

The limit $\lim{x \to 0} \frac{\sin x}{x}$ is a standard limit in calculus which evaluates to 1.

Q: Evaluate $\lim{x \to 0} \frac{\tan x}{x}$.

संबंध $\tan x = \frac{\sin x}{\cos x}$ का उपयोग करके, हमें $\lim{x \to 0} \frac{\sin x}{x \cos x} = \left(\lim{x \to 0} \frac{\sin x}{x}\right) \cdot \left(\lim{x \to 0} \frac{1}{\cos x}\right) = 1 \cdot 1 = 1$ प्राप्त होता है।

Question 1

Evaluate $\lim{x 	o 0} \frac{\sin x}{x}$.

Accepted Answer

The limit $\lim{x 	o 0} \frac{\sin x}{x}$ is a standard limit in calculus which evaluates to 1.

Question 2

Evaluate $\lim{x 	o 0} \frac{	an x}{x}$.

Accepted Answer

संबंध $	an x = \frac{\sin x}{\cos x}$ का उपयोग करके, हमें $\lim{x 	o 0} \frac{\sin x}{x \cos x} = \left(\lim{x 	o 0} \frac{\sin x}{x}ight) \cdot \left(\lim{x 	o 0} \frac{1}{\cos x}ight) = 1 \cdot 1 = 1$ प्राप्त होता है।

Question 3

Evaluate $\lim{x 	o 0} \frac{e^x - 1}{x}$.

Accepted Answer

By definition of the derivative of $e^x$ at $x=0$, the limit evaluates to 1.

Question 4

Evaluate $\lim{x 	o 0} \frac{\log(1+x)}{x}$.

Accepted Answer

This is a standard limit whose value is equal to 1.

Question 5

What is the derivative of $f(x) = x^n$ with respect to $x$?

Accepted Answer

According to the power rule of differentiation, $\frac{d}{dx}(x^n) = n x^{n-1}$.

Limits and Derivatives