Question

Consider the functions ?(?) = 5? + 3 and ?(?) = 3?^2 − 4? + 7....

Consider the functions ?(?) = 5? + 3 and ?(?) = 3?^2 − 4? + 7.

i. Conjecture which is increasing faster. ii. Calculate: ??? ?→∞ 5 ? + 3

iii. Calculate: ??? ?→∞ 3 ?^2 − 4? + 7

iv. By themselves do these two limits answer the question about which is increasing faster?

v. Evaluate using L’Hôpital’s Rule: ??? ?→∞ 5?+3 / 3?^2−4?+7

vi. What does the result of this finished limit calculation tell us about which function is increasing faster?

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