Question

Evaluate the limit as x approaches 0 for the function limˣ→⁰cos(x)x.

A. 0
B. 1/2
C. 1
D. −1
E. Does not exist

Answer 1

The limit as x approaches 0 for the function limˣ→⁰cos(x)x is 1.

Therefore correct answer is C. 1

Step-by-step explanation:

To evaluate the limit as x approaches 0 for the function
`\( \lim_{{x \to 0}} \cos(x)x\)`, the result is 1.

As x approaches 0, the cosine of 0 is 1, and x approaches 0. The product of these two terms,
`\(\cos(x)x\)`, also approaches 0. Therefore, the correct limit is 1.

The limit is found by considering the behavior of the function as x gets arbitrarily close to 0. Since the cosine of 0 is 1, and x approaches 0, the overall limit is 1.

Therefore correct answer is C. 1