Limits Homework HOLLYER Name PS id This is a 112 point assignment Please turn it in as a pdf file to the assignments tab in CourseWare 1 Problem 1 10 points x 2 6x 5 7 x 2 x2 1 Why is lim Include a brief explanation and a table or a graph as further evidence 2 Problem 2 Given 15 points f x 2x 21 x 7 Give the following information the following limits lim f x x 3 lim f x x Domain Range all asymptotes all intercepts and lim f x x 3 lim f x x Sketch the graph by hand or with a graphing program but sure to add the asymptote lines if you re using MathGV I can coach you Attach it right behind this sheet 3 Question 3 Given 15 points f x x 2 4x 4 x2 4 Give the following information the following limits lim f x x 2 Domain Range all asymptotes all intercepts and lim f x x 2 lim f x x 2 lim f x x lim f x x Sketch the graph by hand or with a graphing program show important parts of the graph like asymptotes and intercepts Attach the graph right behind this sheet 4 Question 4 15 points Given the following function x 2 f x x 1 x A x 2 3 x 2 x 3 State the domain the range and all intercepts B Sketch the graph neatly and accurately on an attached separate page C Find lim f x x 3 lim f x x 2 D lim f x x 3 lim f x x 2 lim f x x 3 lim f x x 2 Calculate 1 f 5 f 2 f 5 5 Question 5 Given the following sequence 10 points an 1 n n with n a natural number Give 8 terms of the sequence Sketch a 2D graph of the sequence Discuss bounds and limits Support your assertions with an argument using enclosures like I showed you in class 6 Question 6 10 points f x x What function is this How is this different from the one in the video Where is it continuous Sketch a graph of this function from x 3 to x 3 7 Question 7 f x Given A 15 points x 2 6x 5 x2 1 What s the domain the intercepts all asymptotes and holes B Sketch the graph on an attached separate page C Fill in the following information lim f x x 1 lim f x x 1 D lim f x x 1 lim f x x 1 lim f x f 1 lim f x f 1 x 1 x 1 Where is the function continuous How do you know 8 Question 8 22 points Give the Difference Quotient and Derivative for the following 4 functions Show your work in agonizing detail A f x 3x 2 9 B f x x 2 3x 4 10 C f x 2 x 11 D f x 3x 2 x 12