Question

The value of \[ \lim_{x \to \infty} \left( e^x + e^{-x} - e^x \right) \] is equal to
 

• A. 1
• B. \( e \)
• C. -1
• D. \( \frac{1}{e} \)

Hint:

As \( x \to \infty \), \( e^{-x} \) approaches 0 and can be ignored in the limit.

Answer 1

The Correct Option is C

Step 1: Simplify the expression.
We have: \[ \lim_{x \to \infty} \left( e^x + e^{-x} - e^x \right) \] Simplifying the expression: \[ = \lim_{x \to \infty} e^x - e^x + e^{-x} \] \[ = \lim_{x \to \infty} 0 + e^{-x} \]
Step 2: Evaluate the limit.
As \( x \to \infty \), \( e^{-x} \) approaches 0. Therefore, the limit is: \[ = 0 \]
Step 3: Conclusion.
Therefore, the correct answer is \( \boxed{0} \), and the correct option is (3) -1.