Question
Asked Dec 8, 2019
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20. Given f(x) = [[ 2x – 5|], which statement is TRUE ?
a. f(x) is continuous at x =
b. f(x) is continuous at x =
c. f(x) is continuous at x = 35.2
d. f(x) is continuous at x = – 145
e. f(x) is continuous at = 0
f. f(x) is not continuous at x = 35 from the LEFT
g. f(x) is not continuous at x = 478 from the RIGHT
%3D
2300 from the RIGHT
- 3.5 from the LEFT
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20. Given f(x) = [[ 2x – 5|], which statement is TRUE ? a. f(x) is continuous at x = b. f(x) is continuous at x = c. f(x) is continuous at x = 35.2 d. f(x) is continuous at x = – 145 e. f(x) is continuous at = 0 f. f(x) is not continuous at x = 35 from the LEFT g. f(x) is not continuous at x = 478 from the RIGHT %3D 2300 from the RIGHT - 3.5 from the LEFT

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Expert Answer

Step 1

Double brackets or [[]] in math refer to rounding off the value inside to its greatest integer less than or equal to the value.

To check the limit from the Right of -2300 used limit x-> -2300^+

 

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lim [[2x-5]] x-2300* =[[2(-2300*)-5]] =[[-4600*-5]] =[[-4605* ]]

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Step 2

On the right side of -4605 lets take -4604.99 

Greatest integer less than or equal to -4604.99 is -4605.

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-4605+ =[[-4604.99]] =-4605

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Step 3

f(2300)=-4605 too.

So f(x) is continuous at x=-2300 fr...

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f (2300)=[[2(-2300)-5]]=[[-4600-5]]=[[-4605]]=-4605

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