Find the limit of the function by using direct substitution. limit as x approaches quantity pi divided by two of quantity two times e to the x times cosine of x.

Question

asked Oct 9, 2017 67.8k views

1 Answer

Sportzpikachu · Answer 1 · 2017-10-13T06:51:04+0000

Answer:

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

General Formulas and Concepts:

Pre-Calculus

Calculus

Limits

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

Explanation:

Step 1: Define

Identify

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

Step 2: Evaluate

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

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

Unit: Limits