Use the graph of the function f shown to estimate the indicated quantities to th

Question

Use the graph of the function f shown to estimate the indicated quantities to the nearest integer. Complete parts a through e. a. Find the limit lim x rightarrow 2^- f(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. lim x rightarrow 2^- f(x) _______ B. The limit does not exist. b. Find the limit lim x rightarrow 2^f(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. lim x rightarrow 2^+ f(x) = ______ B. The limit does not exist. c. Find the limit lim x rightarrow 2 f(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. lim x rightarrow 2 f(x) = ______ B. The limit does not exist. d. Find the function value f(2). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. f(2) = ______ B. The value does not exist. e. Is f continuous at x = 2? No Yes

Explanation / Answer

(i) Here we need to find left hand limit as x is approaching 2 from left side of the graph:

Thus limx -> 2- f(x) = 2

(ii) Here we need to find Right hand limit as x is approaching 2 from right side of the graph:

Thus limx -> 2+ f(x) = -1

(iii) Since LHL and RHL are not equal at x=2 thus limx -> 2 f(x) = Doesnt exist.

(iv) f(2) = -1

(iv) Since LHL is not eqaul to RHL thus our graph is discontinous at x=2.

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