Let f(x)=\frac{(x+8)^{2}}{x^{2}-64}. Find a) \lim_{x \Rightarrow -8}f(x), b) \lim_{x \Rightarrow

Harold Kessler

Harold Kessler

Answered question

2021-12-27

Let f(x)=(x+8)2x264. Find a) limx8f(x), b) limx0f(x), and c) limx8f(x).

Answer & Explanation

hysgubwyri3

hysgubwyri3

Beginner2021-12-28Added 43 answers

Step 1
a) Plug the given expression for f(x), then factor the denominator and simplify.
limx8f(x)
=limx8(x+8)2x264
=limx8(x+8)2x282
=limx8(x+8)2(x+8)(x8)
=limx8(x+8)(x8)
Step 2
Plug x=8 for the limit
=limx8(x+8)(x8)
=8+888
=016
=0
eninsala06

eninsala06

Beginner2021-12-29Added 37 answers

Step 3
b) Plug expression of f(x) in the limit then simplify and plug x=0
limx0f(x)
=limx0(x+8)2x264
=limx0(x+8)2x282
=limx0(x+8)2(x+8)(x8)
=limx0(x+8)(x8)
=0+808
=1
karton

karton

Expert2022-01-04Added 613 answers

Step 4
c) We simplify the limit same way and plug x=8 this time.
limx8f(x)=limx8(x+8)2x264=limx8(x+8)2x282=limx8(x+8)2(x+8)(x8)=limx8(x+8)(x8)=8+888=160=DNE

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