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Step 3 Recall the quotient law, which states that if the limits $\lim_{x \to 8} f(x)$ and $\lim_{x \to 8} g(x)$ exist and $\lim_{x \to 8} g(x) \neq 0$, then the following holds. $\lim_{x \to 8} \frac{f(x)}{g(x)} = \frac{\lim_{x \to 8} f(x)}{\lim_{x \to 8} g(x)}$ Applying this limit law gives us the following. $\lim_{x \to 8} \left( \frac{3 + \frac{1}{x} - \frac{x^2}{2}}{\frac{8}{x^2} - 7} \right)$

          Step 3
Recall the quotient law, which states that if the limits $\lim_{x \to 8} f(x)$ and $\lim_{x \to 8} g(x)$ exist and $\lim_{x \to 8} g(x) \neq 0$, then the following holds.
$\lim_{x \to 8} \frac{f(x)}{g(x)} = \frac{\lim_{x \to 8} f(x)}{\lim_{x \to 8} g(x)}$
Applying this limit law gives us the following.
$\lim_{x \to 8} \left( \frac{3 + \frac{1}{x} - \frac{x^2}{2}}{\frac{8}{x^2} - 7} \right)$

Step 3
Recall the quotient law, which states that if the limits limx → 8 f(x) and limx → 8 g(x) exist and limx → 8 g(x) ≠ 0, then the following holds.
limx → 8(f(x))/(g(x)) = (limx → 8 f(x))/(limx → 8 g(x))
Applying this limit law gives us the following.
limx → 8( (3 + (1)/(x) - (x^2)/(2))/((8)/(x^2) - 7))

Added by Ashley G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

12/02/2023

Step 1

Step 1: Recall the given expression: \lim_(x->\infty )((8-(7)/(x^(2)))/((3+(1)/(x)-(3)/(x^(2)))) Show more…

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Step 3 Recall the quotient law, which states that if the limits lim_(x->infty )f(x) and lim_(x->infty )g(x) exist and lim_(x->infty )g(x)!=0, then the following holds. lim_(x->infty )(f(x))/(g(x))=(lim_(x->infty )f(x))/(lim_(x->infty )g(x)) Applying this limit law gives us the following. lim_(x->infty )((8-(7)/(x^(2)))/((3+(1)/(x)-(3)/(x^(2))))=(lim_(x->infty )(1))/(lim_(x->infty )(3+(1)/(x)-(3)/(x^(2)))) Step 3 lim SubmitSkip (you cannot come back) Applying this limit law gives us the following. = X8 :limf(x) X