Question

Evaluate the limit: (lim_{x to [infinity]} {e^x + 1}{e^x}^{3x})

1. (A) 0
2. (B) 1
3. (C) ([infinity])
4. (D) {1}{e^3})

Answer 1

The limit limx→∞(ex+1)(e3x) is ∞.

This correct answer is 3.

Step-by-step explanation:

To evaluate the limit limx→∞(ex+1)(e3x), let's analyze the behavior of the expression as x approaches infinity.

Exponential Growth:

As x goes to infinity, ex and e3x both go to infinity.

Polynomial Growth:

The term (ex +1) also grows to infinity.

Since we have the product of terms that all go to infinity, the limit will be infinity.

Therefore, the correct answer is: (C)∞

This correct answer is 3.