Question 1 Problem 1 (5 points). Consider the function (z+3)' r 5. (a) Is f continuous at r = -17 Explain your answer. (b) Is f continuous at r = 57 Explain your answer. Problem 2 (5 points). Consider the function 9(t) - 210 + 5+3 + 4t + 10 3t + 24t (a) Evaluate the limit lim g(t). (b) Evaluate the limit lim g(t). (c) Does g(t) have any horizontal asymptotes? If so, then write down the equation(s) for these asymptotes. Question 2 Problem 1 (5 points). Let f(x) =4 -x2 and g(x) = 1/Vx. (a) Calculate (go f)(x) and (fog)(z). (b) What are the domains of go f and fog? Problem 2 (5 points). Let f(x) = sin(2x)+1. Write down a function g(r) whose graph is obtained by taking the graph of f(x) and: (a) Shifting it to the right 4 units, and then reflecting it over the r-axis. (b) Vertically stretching it by a factor of 7, and then shifting it up 100 units. Question 3 Problem 1 (5 points). (a) Evaluate the limit lim Vt - 2 if it exists; otherwise, explain why the limit doesn't exist. (b) Evaluate the limit W mi 1 40 2 - VW +4 if it exists; otherwise, explain why the limit doesn't exist. Problem 2 (5 points). Consider the function f(u) = US-4 1 - 94 23-4 (a) Evaluate the limit lim f(u), if it exists; otherwise, explain why the limit doesn't exist. (b) Evaluate the limit lim f(u), if it exists; otherwise, explain why the limit doesn't exist