Question

1. Given that $\lim_{x \to 2} f(x) = 4$ $\lim_{x \to 2} g(x) = -2$ $\lim_{x \to 2} h(x) = 0$ find the limits that exist. If the limit does not exist, explain why. (a) $\lim_{x \to 2} [f(x) + 5g(x)]$ (b) $\lim_{x \to 2} [g(x)]^3$ (c) $\lim_{x \to 2} \sqrt{f(x)}$ (d) $\lim_{x \to 2} \frac{3f(x)}{g(x)}$ (e) $\lim_{x \to 2} \frac{g(x)}{h(x)}$ (f) $\lim_{x \to 2} \frac{g(x)h(x)}{f(x)}$

          1. Given that
$\lim_{x \to 2} f(x) = 4$
$\lim_{x \to 2} g(x) = -2$
$\lim_{x \to 2} h(x) = 0$
find the limits that exist. If the limit does not exist, explain
why.
(a) $\lim_{x \to 2} [f(x) + 5g(x)]$
(b) $\lim_{x \to 2} [g(x)]^3$
(c) $\lim_{x \to 2} \sqrt{f(x)}$
(d) $\lim_{x \to 2} \frac{3f(x)}{g(x)}$
(e) $\lim_{x \to 2} \frac{g(x)}{h(x)}$
(f) $\lim_{x \to 2} \frac{g(x)h(x)}{f(x)}$

1. Given that
limx → 2 f(x) = 4
limx → 2 g(x) = -2
limx → 2 h(x) = 0
find the limits that exist. If the limit does not exist, explain
why.
(a) limx → 2 [f(x) + 5g(x)]
(b) limx → 2 [g(x)]^3
(c) limx → 2√(f(x))
(d) limx → 2(3f(x))/(g(x))
(e) limx → 2(g(x))/(h(x))
(f) limx → 2(g(x)h(x))/(f(x))

Added by Joshua S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

02/14/2023

Step 1

Use standard limit laws: sums and constant multiples pass to the limit, products and powers pass to the limit, a quotient passes to the limit only if the denominator limit ≠ 0, and composition with a continuous function passes to the limit. Show more…

Show all steps

Thanks for your feedback!

1. Given that lim f(x) = 4 X-2 find the limits that exist. If the limit does not exist, explain why. (a) lim [f(x) + 5g(x)] X-2 (c) lim √f(x) X-2 lim g(x) = -2 x → 2 g(x) x-2 h(x) (e) lim lim h(x) = 0 X-2 (b) lim [g(x)]³ X-2 3f(x) x-2 g(x) (d) lim (f) lim g(x) h(x) X-2 f(x) 3- ap 1.Given that lim fx=4 lim gx=-2 limh(x=0 32 find the limits that exist. If the limit does not exist,explain why. alim[fx+5gx] (blim[gx]3 3f(x dlim x2 g(x) clim fx 3 g(x) e lim xhx gxhx) flim x-2 f(x) ap