Answer :
Answer:
[tex]\displaystyle \lim_{x \to \frac{\pi}{2}} 2e^x \cos (x) = 0[/tex]
General Formulas and Concepts:
Pre-Calculus
- Unit Circle
Calculus
Limits
Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \lim_{x \to \frac{\pi}{2}} 2e^x \cos (x)[/tex]
Step 2: Evaluate
- Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to \frac{\pi}{2}} 2e^x \cos (x) = 2e^{\frac{\pi}{2}} \cos(\frac{\pi}{2})[/tex]
- Simplify: [tex]\displaystyle \lim_{x \to \frac{\pi}{2}} 2e^x \cos (x) = 0[/tex]
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits