Math 1A Midterm 2 Practice 1 PDF

MATH 1A MIDTERM 2 (PRACTICE 1) PROFESSOR PAULIN INSTRUCTIONS Do not turn over until instructed to do so. Write your name and SID in the spaces provided on one side of every page of the exam. This exam consists o...

MATH 1A MIDTERM 2 (PRACTICE 1) PROFESSOR PAULIN INSTRUCTIONS Do not turn over until instructed to do so. Write your name and SID in the spaces provided on one side of every page of the exam. This exam consists of 5 questions. You have 1 hours to complete this exam. This exam will be electronically scanned. Do not add or remove any pages from the exam. There is an extra blank page for scratch work on the back of the exam. It can also be used as extra space to write formal solutions as long as everything is clearly labelled. Calculators are not permitted. Show as much working as possible. Even if you don’t end up with the correct answer, you may still get partial credit. Answers without justification will be viewed with suspicion and will not receive credit. Name: Student ID: GSI Name: Math 1A Midterm 2 (Practice 1) PLEASE TURN OVER Name: SID: 1. (30 points) (a) Using the limit definition of the derivative to calculate the derivative of the function p f (x) = 2 x. Solution x+3 (b) Show that the line y = 2 is a tangent line to some point on the graph y = f (x). Solution PLEASE TURN OVER Name: SID: 2. (30 points) Determine the derivatives of the following functions (you do not need to use the limit definition and you do not need to simplify your answer). (a) cos(x2 ) sin(ex ) Solution (b) x1/x ln(x) p x Solution PLEASE TURN OVER Name: SID: 3. (30 points) Consider the curve given by the equation 4x2 +y 2 = 4. Determine all tangent lines to this curve which pass through the point (2, 0). Solution PLEASE TURN OVER Name: SID: 4. (30 points) Sketch the following curve. Be sure to indicate asymptotes, local maxima and minima and concavity. Show your working on this page and draw the graph on the next page. e2x y= x Solution PLEASE TURN OVER Name: SID: Solution (continued) PLEASE TURN OVER Name: SID: 5. (30 points) What is the minimum area of a triangle bounded by the x-axis, y-axis and a straight line passing through ( 3, 5) with positive slope? Solution PLEASE TURN OVER Name: SID: Blank Page PLEASE TURN OVER Name: SID: Blank Page END OF EXAM