MATH 101 Exam 2, Spring 2001

MATHIO1 9/5/01 Second Semester,00-01 QUIZ 2 1. Find dy/dx in each case: ajy= tan?x — secx ob) y = x’sin(2x") ce) y= (3 + co0s*xy"? d) x? + xy ty’ -5x=2 Keyy= () l+x 2. Find equations for the lines tangent and normal to the curve x? + y’ = 2 at the point (1,1). x 3. Use the chain mule to find dw/ds at s = 0 if w= sin(vr - 2) and r = 8sin(s +*). 4. Given the function f (x) = xe- 3x", on (- 0,3}. a) Find the intervals on which the function is increasing and decreasing. b) Identify the function’s local extreme values, if any, saying what they are and where they are taken on. c) Which, if any, of the extreme values are absolute? 5. a) Define the derivative of a function f(x) atx =c. b) Use the definition in (a) to find the derivative of f (x) = 3x7 + Latx=c. Bx + 1x<l 4,x>1 differentiable at x =1? Explain. is continuous at x =1. Is g (x) c) The function g (x) “| nee ERICAN ESN Dhsit ay LIBRARY OF BEIRTy