Question

Find the limit: lim e−9x sin x x→0

Answer 1

Answer:

$\displaystyle \lim_{x \to 0} e^\big{-9x} \sin x = 0$

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

$\displaystyle \lim_{x \to 0} e^\big{-9x} \sin x$

Step 2: Evaluate

1. Limit Rule [Variable Direct Substitution]:                                                     $\displaystyle \lim_{x \to 0} e^\big{-9x} \sin x = e^\big{-9(0)} \sin(0)$
2. Simplify:                                                                                                         $\displaystyle \lim_{x \to 0} e^\big{-9x} \sin x = 0$

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

Unit: Limits