Answer the fоllоwing questiоns, in order on sepаrаte pаper showing all steps necessary to arrive at your solution. Solutions with no work will receive no credit. Give exact answers unless otherwise asked to provide an approximate answer. You may not use a computer algebra system for any portion of this examination. Once you have finished the examination, you will have 10 minutes after logging out of the exam to submit your responses to the Examination 1 Submission Link in Brightspace. Submit your work as a single .pdf file only: submissions that are not submitted as a single .pdf file will not be accepted. ----------------------------- (1) (8 points) Approximate the limit using a table of values with x = -0.0001, -0.001, -0.01, 0.01, 0.001, and 0.0001. limx→0ex-1x{"version":"1.1","math":"limx→0ex-1x"}. (2) (8 points) Suppose the graph of g(x) is given below. Find the following: (3) (12 points) Let "m" be a real number. Given the function below. f(x)=x2-3x,if x≤1,mx3-8,if x>1.{"version":"1.1","math":"f(x)=x2-3x,if x≤1,mx3-8,if x>1."} Find the following: (a) limx→1-fx{"version":"1.1","math":"limx→1-fx"} (b) limx→1+fx{"version":"1.1","math":"limx→1+fx"} (c) Find the value of "m" for which the two-sided limit, limx→1fx{"version":"1.1","math":"limx→1fx"} exists. Problems (4) - (7): (20 points) Find the limit using limit laws and algebra. DO NOT USE A TABLE OF VALUES. DO NOT GIVE AN APPROXIMATION. (4) limx→32x2-4x+cosπx{"version":"1.1","math":"limx→32x2-4x+cosπx"} (5) limx→102x-20x2-8x-20{"version":"1.1","math":"limx→102x-20x2-8x-20"} (6) limx→4x-4x-2{"version":"1.1","math":"limx→4x-4x-2"} (7) limx→515-1xx-5{"version":"1.1","math":"limx→515-1xx-5"} (8) (8 points) Show that the limit does not exist: limx→1x-1x-1{"version":"1.1","math":"limx→1x-1x-1"}. (9) (12 points) Use any method to evaluate each of the following limits. If the limit does not exist, justify why it does not exist. (a) limx→3+2x-3{"version":"1.1","math":"limx→3+2x-3"} (b) limx→3-2x-3{"version":"1.1","math":"limx→3-2x-3"} (c) limx→32x-3{"version":"1.1","math":"limx→32x-3"} Problems (10) - (13): (20 points) Evaluate the limit. Show your work. Do not use a table of values. (10) limx→∞4+2x+4x35x-12x3{"version":"1.1","math":"limx→∞4+2x+4x35x-12x3"} (11) limx→∞x8-7x9+x7-6{"version":"1.1","math":"limx→∞x8-7x9+x7-6"} (12) limx→∞x2-4x2x+3{"version":"1.1","math":"limx→∞x2-4x2x+3"} (13) limx→-∞x2-4x2x+3{"version":"1.1","math":"limx→-∞x2-4x2x+3"} (14) (12 points) Given the function: f(x)=x-7x2-4x+3{"version":"1.1","math":"f(x)=x-7x2-4x+3"}. (a) Determine the domain where the following function is continuous. Write your response in the interval notation. (b) Determine the vertical asymptote(s). Write your answer(s) in the form x = ... . (c) Determine the horizontal asymptote(s). Write your answer(s) in the form y = ... . DO NOT TYPE RESPONSES IN THE FIELD BELOW.
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