Question

Find the limit. lim θ→0 sin(3θ) θ + tan(4θ)

Answer 1

Answer:

$\displaystyle \lim_{\theta \to 0} \sin (3\theta)\theta + \tan (4\theta) = 0$

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

$\displaystyle \lim_{\theta \to 0} \sin (3\theta)\theta + \tan (4\theta)$

Step 2: Evaluate

1. Limit Rule [Variable Direct Substitution]:                                                    $\displaystyle \lim_{\theta \to 0} \sin (3\theta)\theta + \tan (4\theta) = \sin(0) \cdot 0 + tan(0)$
2. Simplify:                                                                                                         $\displaystyle \lim_{\theta \to 0} \sin (3\theta)\theta + \tan (4\theta) = 0$

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

Unit: Limits