Question
Asked Dec 22, 2019
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if x < 1
if x = 1
4
g(x):
2 - x2 if 1 < x< 2'
if x > 2
(a) Evaluate each of the following, if it exists. (If an answer does not exist, enter DNE.)
lim g(x)
(i)
lim g(x)
(ii)
(iii)
g(1)
lim g(x)
(iv)
lim g(x)
(v)
lim g(x)
(vi)
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if x < 1 if x = 1 4 g(x): 2 - x2 if 1 < x< 2' if x > 2 (a) Evaluate each of the following, if it exists. (If an answer does not exist, enter DNE.) lim g(x) (i) lim g(x) (ii) (iii) g(1) lim g(x) (iv) lim g(x) (v) lim g(x) (vi)

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Expert Answer

Step 1

Given function is

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if x <1 х | 4 g(x)=. if x = 1 2-x if1<x<2 х — 3 ifx >2

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Step 2

Evaluating, we get

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(i) To find lim g(x) since for values less than 1, g(x) = x Hence, lim g(x) = lim(x) =1 lim g(x) =1

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Step 3
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(ii) To find lim g (x) x→1* since for values greater than 1, 8(x) =2-x² Hence, lim g(x) = lim(2 -x²) x- = 2-1 lim g(x)=1

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Tagged in

Math

Calculus

Functions