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11. Do the following (a) Let f : (c, d) → R, and let a E (c, d). Prove that if lim,f(x) = L then lim, a+ f(x) = L and lim, - f(x) = L. (b) Let g : R-R be defined as below. Compute lim,2 9(x) or explain why this limit does not exist. You may use the result of exercise (a) and the fact that a linear function is continuous on R. (c) Is the function g defined below continuous at 2? Justify your answer. (d) Does g'(2) exist for the function g defined below? Justify your answer. 4r-3 if r<2 g(z) = 6 if z = 2 2r +1 if r> 2.

11. Do the following (a) Let f : (c, d) → R, and let a E (c, d). Prove that if lim,f(x) = L then lim, a+ f(x) = L and lim, - f(x) = L. (b) Let g : R-R be defined as below. Compute lim,2 9(x) or explain why this limit does not exist. You may use the result of exercise (a) and the fact that a linear function is continuous on R. (c) Is the function g defined below continuous at 2? Justify your answer. (d) Does g'(2) exist for the function g defined below? Justify your answer. 4r-3 if r<2 g(z) = 6 if z = 2 2r +1 if r> 2.

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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11. Do the following (a) Let f : (c, d) - R, and let a E (c, d). Prove that if lim, a f(r) = L then lim,-a+ f(x) = L and lim, a- f(x) = L. (b) Let g : R – R be defined as below. Compute lim,-2 g(x) or explain why this limit does not exist. You may use the result of exercise (a) and the fact that a linear function is continuous on R. (c) Is the function g defined below continuous at 2? Justify your answer. (d) Does g'(2) exist for the function g defined below? Justify your answer. 4x – 3 if r < 2 g(r) = { 6 if z = 2 2r +1 if z > 2.
Transcribed Image Text:11. Do the following (a) Let f : (c, d) - R, and let a E (c, d). Prove that if lim, a f(r) = L then lim,-a+ f(x) = L and lim, a- f(x) = L. (b) Let g : R – R be defined as below. Compute lim,-2 g(x) or explain why this limit does not exist. You may use the result of exercise (a) and the fact that a linear function is continuous on R. (c) Is the function g defined below continuous at 2? Justify your answer. (d) Does g'(2) exist for the function g defined below? Justify your answer. 4x – 3 if r < 2 g(r) = { 6 if z = 2 2r +1 if z > 2.
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