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Define the function f(x) to be 1/x for x for all x that are (2n,2n+1) for even n and -1/x for x for all x that are you (2n, 2n+1) for odd n. Graph the function and describe for which points limit do not exist. Does the limit exist as x goes to infinity? (The n here represents natural numbers e.g. 0,1,2,...27,... and hence the first interval is (0,1], the second is (1,2], etc.)

Question

Define the function f(x) to be 1/x for x for all x that are (2n,2n+1) for even n and -1/x for x for all x that are you (2n, 2n+1) for odd n. Graph the function and describe for which points limit do not exist. Does the limit exist as x goes to infinity? (The n here represents natural numbers e.g. 0,1,2,...27,... and hence the first interval is (0,1], the second is (1,2], etc.) 

check_circleAnswer
Step 1

The given function is

1
(2n, 21)ne even
f(x)
1
(2n, 2n
ne odd
where n 0,1,2,3,4....
help_outline

Image Transcriptionclose

1 (2n, 21)ne even f(x) 1 (2n, 2n ne odd where n 0,1,2,3,4....

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Step 2

To draw the graph for the given function.

To determine the value of limit as x approaches to infinity.

To find the points for which the limit doesn’t exist.

Step 3

 The given function ...

(0,1)(4,5)(8,9)
x
f(x)
1
(2,3)(6,7)(10,11) .
help_outline

Image Transcriptionclose

(0,1)(4,5)(8,9) x f(x) 1 (2,3)(6,7)(10,11) .

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Tagged in

Math

Calculus

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