Question

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

Answer 1

`\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`

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