Consider the function given below.1x2COsf(x)x-2=0.x22Complete parts (a) through (c)-1-(a) Does limf(x) exist? If so, what is it? If not, why not?J.x 2O A. Yes, lim f(x)(Simplify your answer.)x+2O B. No, because there is no real number to which the function's values stay increasingly close as x approaches 2 from the left side.(b) Does limx 2+f(x) exist? If so, what is it? If not, why not?O A. Yes, lim f(x). (Simplify your answer.)-x 2O B. No, because there is no real number to which the function's values stay increasingly close as x approaches 2 from the right side.(c) Does lim f(x) exist? If so., what is it? If not, why not?

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Asked Sep 9, 2019
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Consider the function given below.
1
x2
COs
f(x)
x-2
=
0.
x22
Complete parts (a) through (c)
-1-
(a) Does lim
f(x) exist? If so, what is it? If not, why not?
J.
x 2
O A. Yes, lim f(x)
(Simplify your answer.)
x+2
O B. No, because there is no real number to which the function's values stay increasingly close as x approaches 2 from the left side.
(b) Does lim
x 2+
f(x) exist? If so, what is it? If not, why not?
O A. Yes, lim f(x)
. (Simplify your answer.)
-
x 2
O B. No, because there is no real number to which the function's values stay increasingly close as x approaches 2 from the right side.
(c) Does lim f(x) exist? If so., what is it? If not, why not?
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Consider the function given below. 1 x2 COs f(x) x-2 = 0. x22 Complete parts (a) through (c) -1- (a) Does lim f(x) exist? If so, what is it? If not, why not? J. x 2 O A. Yes, lim f(x) (Simplify your answer.) x+2 O B. No, because there is no real number to which the function's values stay increasingly close as x approaches 2 from the left side. (b) Does lim x 2+ f(x) exist? If so, what is it? If not, why not? O A. Yes, lim f(x) . (Simplify your answer.) - x 2 O B. No, because there is no real number to which the function's values stay increasingly close as x approaches 2 from the right side. (c) Does lim f(x) exist? If so., what is it? If not, why not?

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Expert Answer

Step 1

Consider the given expression:

1
cos
x-2
f(x)
0
,.r22
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1 cos x-2 f(x) 0 ,.r22

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Step 2

The limit of the function at a point x=a exists if

lim f(x)- lim f(x)-f(a)
xa
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lim f(x)- lim f(x)-f(a) xa

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Step 3

Check the continuity of the function at a point x=2 then calcula...

f(x)
RHL-lim
xa
lim (0)
x-2
=0
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f(x) RHL-lim xa lim (0) x-2 =0

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