Mathematics 31B Practice Midterm 1 Exam Date October 22 2012 Instructor D E Weisbart NAME please print legibly Your University ID Number Your Discussion Section and TA Signature There are SEVEN questions on this examination Calculators notes and books may not be used in this examination You may not receive full credit for a correct answer if insufficient work is shown QUESTION VALUE SCORE 1 12 2 12 3 12 4 12 5 12 6 12 7 12 TOTAL 84 1 1 12 points a Simplify the following expression in terms of ln 2 and ln 5 Compute ln 209 Answer b Your answer to the following question should be expressed as a whole number Compute 3 e ln 10 ln 2 Answer c Compute lim n 1 4 3n 2n Answer 2 2 12 points a Suppose that f x is differentiable that f 3 8 and that f 0 3 4 Then 0 f 1 8 Answer b Suppose that f x is differentiable that f 2 4 and that f 0 2 21 Find the equation for the line tangent to the graph of f 1 x at the point 4 2 Answer 3 3 12 points a Compute the derivative of the function f x ln x2 2 e2x 2 x Answer b Compute the derivative of the function 2 f x log4 xe3x Answer c Compute the derivative of the function f x x2 5x 1 2x 1 Answer 4 4 12 points a Suppose that y 0 x 2y 1 and y 0 10 Compute y 4 Answer b A radioactive isotope has half life 100 years If you initially have 100 grams of the material how much will you have after 750 years Answer c Your friend gives you and unknown amount of a radioactive isotope After 2 years you have 100 grams and after 4 years you have 80 grams How much will you have after 10 years Answer 5 5 12 points a Can you use l Hopital s rule to calculate the following limit x2 1 x 1 x 1 lim Answer b 2 ex e lim x 1 x 1 Answer c ln x x x lim Answer 6 6 12 points a Z 2x2 e3x dx Answer b Z ln 3x dx Answer 7 7 12 points a Z e2x sin 3x dx Answer b 1 Z 0 1 dx 2 9x2 Answer c Z 1 1 1 dx 2 x2 Answer 8