Determine whether the following statements are true and give an explanation or counterexample. a. By lHpitals Rule,

Question:

Determine whether the following statements are true and give an explanation or counterexample.

a. By l’Hôpital’s Rule,2 х lim х—2 х2 — 1 lim x→2 2x

b. lim (x sin x) = lim f(x)g(x) lim f'(x)lim g'(x) = (lim 1)(lim cos x) = 1. х—0 х>0 х—0 `x→0 `x→0   

c. is an indeterminate form.

d. The number 1 raised to any fixed power is 1. Therefore, because (1 + x) → 1 as x → 0, 1 + x)1/x →1 as x→0.

e. The functions ln x100 and ln x have comparable growth rates as x→∞.

f. The function ex grows faster than 2x as x→∞.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For  book-img-for-question

Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Question Posted: