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Answer:

\(\displaystyle \lim_{x \to \frac{\pi}{2}} 2e^x \cos (x) = 0\)

General Formulas and Concepts:

Pre-Calculus

  • Unit Circle

Calculus

Limits

Limit Rule [Variable Direct Substitution]:                                                            \(\displaystyle \lim_{x \to c} x = c\)

Step-by-step explanation:

Step 1: Define

Identify

\(\displaystyle \lim_{x \to \frac{\pi}{2}} 2e^x \cos (x)\)

Step 2: Evaluate

  1. Limit Rule [Variable Direct Substitution]:                                                    \(\displaystyle \lim_{x \to \frac{\pi}{2}} 2e^x \cos (x) = 2e^{\frac{\pi}{2}} \cos(\frac{\pi}{2})\)
  2. Simplify:                                                                                                         \(\displaystyle \lim_{x \to \frac{\pi}{2}} 2e^x \cos (x) = 0\)

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

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