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

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

a. By l’Hôpital’s Rule,

b.   

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 e^x grows faster than 2^x as x→∞.

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2 х lim х—2 х2 — 1 lim x→2 2x 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