Let f(x)=(x+8)2x2−64. Find a) limx⇒−8f(x), b) limx⇒0f(x), and c) limx⇒8f(x).

Step 1 a) Plug the given expression for f(x), then factor the denominator and simplify. limx⇒−8f(x) =limx⇒−8(x+8)2x2−64 =limx⇒−8(x+8)2x2−82 =limx⇒−8(x+8)2(x+8)(x−8) =limx⇒−8(x+8)(x−8) Step 2 Plug x=−8 for the limit =limx⇒−8(x+8)(x−8) =−8+8−8−8 =0−16 =0

Step 3 b) Plug expression of f(x) in the limit then simplify and plug x=0 limx⇒0f(x) =limx⇒0(x+8)2x2−64 =limx⇒0(x+8)2x2−82 =limx⇒0(x+8)2(x+8)(x−8) =limx⇒0(x+8)(x−8) =0+80−8 =−1

Step 4 c) We simplify the limit same way and plug x=8 this time. limx⇒8f(x)=limx⇒8(x+8)2x2−64=limx⇒8(x+8)2x2−82=limx⇒8(x+8)2(x+8)(x−8)=limx⇒8(x+8)(x−8)=8+88−8=160=DNE

Step 1 a) Plug the given expression for f(x), then factor the denominator and simplify. limx⇒−8f(x) =limx⇒−8(x+8)2x2−64 =limx⇒−8(x+8)2x2−82 =limx⇒−8(x+8)2(x+8)(x−8) =limx⇒−8(x+8)(x−8) Step 2 Plug x=−8 for the limit =limx⇒−8(x+8)(x−8) =−8+8−8−8 =0−16 =0

Step 3 b) Plug expression of f(x) in the limit then simplify and plug x=0 limx⇒0f(x) =limx⇒0(x+8)2x2−64 =limx⇒0(x+8)2x2−82 =limx⇒0(x+8)2(x+8)(x−8) =limx⇒0(x+8)(x−8) =0+80−8 =−1

Step 4 c) We simplify the limit same way and plug x=8 this time. limx⇒8f(x)=limx⇒8(x+8)2x2−64=limx⇒8(x+8)2x2−82=limx⇒8(x+8)2(x+8)(x−8)=limx⇒8(x+8)(x−8)=8+88−8=160=DNE

We have an answer to "Let f(x)=(x+8)2x2−64. Find a) limx⇒−8f(x), b) limx⇒0f(x), and..."

Harold Kessler

Answered question

2021-12-27

Let

f (x) = \frac{{(x + 8)}^{2}}{x^{2} - 64}

. Find a)

lim_{x \Rightarrow - 8} f (x)

, b)

lim_{x \Rightarrow 0} f (x)

, and c)

lim_{x \Rightarrow 8} f (x)

Answer & Explanation

hysgubwyri3

Beginner2021-12-28Added 43 answers

Step 1
a) Plug the given expression for

f (x)

, then factor the denominator and simplify.

lim_{x \Rightarrow - 8} f (x)

= lim_{x \Rightarrow - 8} \frac{{(x + 8)}^{2}}{x^{2} - 64}

= lim_{x \Rightarrow - 8} \frac{{(x + 8)}^{2}}{x^{2} - 8^{2}}

= lim_{x \Rightarrow - 8} \frac{{(x + 8)}^{2}}{(x + 8) (x - 8)}

= lim_{x \Rightarrow - 8} \frac{(x + 8)}{(x - 8)}

Step 2
Plug

x = - 8

for the limit

= lim_{x \Rightarrow - 8} \frac{(x + 8)}{(x - 8)}

= \frac{- 8 + 8}{- 8 - 8}

= \frac{0}{- 16}

= 0

eninsala06

Beginner2021-12-29Added 37 answers

Step 3
b) Plug expression of

f (x)

in the limit then simplify and plug

x = 0

lim_{x \Rightarrow 0} f (x)

= lim_{x \Rightarrow 0} \frac{{(x + 8)}^{2}}{x^{2} - 64}

= lim_{x \Rightarrow 0} \frac{{(x + 8)}^{2}}{x^{2} - 8^{2}}

= lim_{x \Rightarrow 0} \frac{{(x + 8)}^{2}}{(x + 8) (x - 8)}

= lim_{x \Rightarrow 0} \frac{(x + 8)}{(x - 8)}

= \frac{0 + 8}{0 - 8}

= - 1

karton

Expert2022-01-04Added 613 answers

Step 4
c) We simplify the limit same way and plug x=8 this time.
$\begin{matrix} lim_{x \Rightarrow 8} f (x) \\ = lim_{x \Rightarrow 8} \frac{(x + 8)^{2}}{x^{2} - 64} \\ = lim_{x \Rightarrow 8} \frac{(x + 8)^{2}}{x^{2} - 8^{2}} \\ = lim_{x \Rightarrow 8} \frac{(x + 8)^{2}}{(x + 8) (x - 8)} \\ = lim_{x \Rightarrow 8} \frac{(x + 8)}{(x - 8)} \\ = \frac{8 + 8}{8 - 8} \\ = \frac{16}{0} \\ = D N E \end{matrix}$

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