The value of the limit of x/cosx is equal to 0 when x approaches to 0. Here we will learn how to find the limit of x/cosx when x tends 0. The formula of x/cosx limit as x goes to 0 is given below:
limx→0 $\dfrac{x}{\cos x}$ = 0.
Proof of limit x/cosx is 0 when x→0
We can directly show the limit of x/cosx is equal to zero when x→0. We proceed as follows.
limx→0 $\dfrac{x}{\cos x}$
= $\dfrac{\lim\limits_{x \to 0} x}{\lim\limits_{x \to 0} \cos x}$ by the quotient rule of limits.
= $\dfrac{0}{\cos 0}$
= $\dfrac{0}{1}$ as the value of cos0 is 1.
= 0
So the limit of x/cosx is equal to 0 when x approaches to 0.
NOTE:
By the same technique, we can show that
• the limit of x/cos2x is equal to 0 as x tends to 0, that is, limx→0 $\dfrac{x}{\cos 2x}$ = 0.
• limx→0 $\dfrac{x}{\cos ax}$ = 0 for any number a.
• limx→0 $\dfrac{2x}{\cos x}$ = 0.
ALSO READ:
Epsilon-delta definition of limit
FAQs
Q1: What is the limit of x/cosx when x approaches 0?
Answer: The limit of x/cosx is equal to 0 when x approaches to 0, that is, limx→0 (x/cosx) = 0.