Respuesta :

Space

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

  1. 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]
  2. 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

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