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Answer :

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Answer:

[tex]\displaystyle \lim_{x \to 0} e^\big{-9x} \sin 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 0} e^\big{-9x} \sin x[/tex]

Step 2: Evaluate

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

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

Unit: Limits

Go Teaching: Other Questions