Question

Determine the limit of x^2 sin (1/2) as z approaches 0.

a. 0
b. 1
c. -1
d. The limit does not exist

Answer 1

The limit of x^2 sin(1/2) as z approaches 0 is 0 because the constant sin(1/2) does not affect the limit of x^2 as x approaches 0, which is 0.

Step-by-step explanation:

The question asks to determine the limit of x2 sin(1/2) as z approaches 0. We can note that sin(1/2) is a constant value, since it does not depend on z or x. Thus, the limit can be found by taking the limit of x2 alone, as z approaches 0. This is because the function x2 multiplied by a constant will just affect the overall multiplication without affecting the limit process. Since the limit of x2 as z approaches 0 is 0, the entire expression's limit will be 0 times the constant sin(1/2), which is simply 0. Therefore, the answer is (a) 0.