Question

find the indicated limit if it exists

Answer 1

Answer:

$\displaystyle \lim_{x \to \infty} \frac{x^2}{1 + 3x + 5x^2} = \frac{1}{5}$

General Formulas and Concepts:

Calculus

• Limits

Step-by-step explanation:

Step 1: Define

$\displaystyle \lim_{x \to \infty} \frac{x^2}{1 + 3x + 5x^2}$

Step 2: Determine Rule

If the highest power of x in a rational expression is the same both numerator and denominator, then the limit as x approached ∞ would be the highest term coefficient in the numerator divided by the highest term coefficient in the denominator.

Step 3: Identify

Numerator highest power: x²

• Coefficient: 1

Denominator highest power: 5x²

• Coefficient: 5

Step 4: Evaluate

Apply rule.

$\displaystyle \lim_{x \to \infty} \frac{x^2}{1 + 3x + 5x^2} = \frac{1}{5}$

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

Unit: Limits

Book: College Calculus 10e