Question

Please help!! i have no clue what to do and this packet is due tonight.

Answer 1

Answer:

[D] ∞

General Formulas and Concepts:

Calculus

Limits

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \lim_{n \to \infty} s(n)$

$\displaystyle s(n) = (\frac{5}{4n^4})(3n^5 + 3n^4 + 2n^3 + n^2)$

Step 2: Evaluate

1. Substitute in function [Limit]:                                                                           $\displaystyle \lim_{n \to \infty} (\frac{5}{4n^4})(3n^5 + 3n^4 + 2n^3 + n^2)$
2. Multiply:                                                                                                             $\displaystyle \lim_{n \to \infty} \frac{5(3n^5 + 3n^4 + 2n^3 + n^2)}{4n^4}$
3. Power Method:                                                                                                 $\displaystyle \lim_{n \to \infty} \frac{5(3n^5 + 3n^4 + 2n^3 + n^2)}{4n^4} = \infty$

Since the degree of the polynomial is greater in the numerator than in the denominator, the top will always increase faster than the bottom, thus getting infinitely larger.

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

Unit: Limits

Book: College Calculus 10e