First slide

Introduction to limits

Question

If $\lim_{x \to 0} \frac{p \cos x + x e^{\frac{1}{x}}}{1 + \sin x + q \cos x . e^{\frac{1}{x}}} = 0$ , then which of the following is/are incorrect about p, q ?

Moderate

A

$p = 0, q \in R$
B

$p = 4, q = 2$
C

$p = 2, q \in R$
D

$p = 0, q = 2$

Solution

$\lim_{x \to 0^{+}} \frac{\frac{p \cos x}{e^{\frac{1}{x}}} + x}{\frac{1 + \sin x}{e^{\frac{1}{x}}} + q \cos x} = 0 \Rightarrow q \in R - {0}$ $\lim_{x \to 0^{-}} \frac{p \cos x + x e^{\frac{+ 1}{x}}}{1 + \sin x + q \cos x e^{\frac{1}{x}}} \Rightarrow p = 0$

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