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Find the following limit or state that it does not exist. Assume b is a fixed real number.((x-b)^(20)-2x+2b)/(x-b)

Question

Find the following limit or state that it does not exist. Assume b is a fixed real number.

((x-b)^(20)-2x+2b)/(x-b)

check_circleAnswer
Step 1

Obtain the limit assuming b is a fixed number as,

(-b+x) +2-x+b)
20
((x-b)-2x2b)
lim
=lim
(x-b)
(x-b)
x-b
xb
(-b+x)(-b+x)-2(-b+x)
=lim
19
(x-b)
xb
(-b+x((-b+x)2
(x-b)
19
- 2
= lim
x-b
=lim
help_outline

Image Transcriptionclose

(-b+x) +2-x+b) 20 ((x-b)-2x2b) lim =lim (x-b) (x-b) x-b xb (-b+x)(-b+x)-2(-b+x) =lim 19 (x-b) xb (-b+x((-b+x)2 (x-b) 19 - 2 = lim x-b =lim

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Step 2

On further simpli...

((x-b)-2x+2)(b-b)-2)
19
lim
(x-b)
xb
(0-2)
=-2
help_outline

Image Transcriptionclose

((x-b)-2x+2)(b-b)-2) 19 lim (x-b) xb (0-2) =-2

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