Question

The limit as x approaches 0 of sin^4(x) times e to the x power minus 1 is

a) 0
b) 1
c) -1
d) [infinity]

Answer 1

The limit as x approaches 0 of sin^4(x) times e^(x-1) is 0.

Step-by-step explanation:

To find the limit as x approaches 0 of sin^4(x) * e^(x-1), we can use the limit properties and evaluate it step by step. Let's break it down:

1. First, the limit of sin(x) as x approaches 0 is 0, since the sine function approaches 0 for small values of x.
2. The limit of e^(x-1) as x approaches 0 is e^(0-1) = e^(-1), since any number raised to the power of 0 is 1, and e^0 = 1 / e = e^(-1).
3. Now, we can multiply the limits together: 0 * e^(-1) = 0. Therefore, the limit of the given expression as x approaches 0 is 0.