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Unformatted text preview: Math 151, Fall 2009, Review Problems for the Final Exam Your final exam is likely to have problems that do not resemble these review problems. You should also look at the review problems for the first two exams. (1) Find the largest interval [ a,b ] such that sin x 3cos x for all x in [ a,b ]. Find the area of the region bounded by y = sin x , y = 3cos x between x = a and x = b . (2) A continuous function f ( x ) on the interval [1 , 10] has the properties R 8 1 f ( x ) dx = 14, R 10 4 f ( x ) dx = 7, R 10 1 f ( x ) dx = 2. Find R 8 4 f ( x ) dx . (3) Evaluate Z (1 + x )(2 + 3 x ) dx , Z 2 3 2 + 3 x 2 x dx , Z 2 1  x 1  dx . (4) Find Z x 2 e x 3 +4 dx , Z sin x cos xdx , Z tan x sec 2 xdx . (5) A bacterial population quadruples in size every 7 days. How many days does it take for this population to triple in size? (6) Explain why the function f ( x ) = n 2 x + 1 if x 1, 4 x 1 if x > 1 is continuous but not differen tiable. (7) A continuous function f ( x ) is defined by f ( x ) =  x  ln  x  if x 6 = 0, a if x = 0, where a is a constant. Find a . Is f ( x ) a differentiable function? Find the intervals where f ( x ) is increasing and the intervals where f ( x ) is decreasing. Hint: Look at the case x 0 and...
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This note was uploaded on 01/18/2012 for the course MATH 151 taught by Professor Sc during the Spring '08 term at Rutgers.
 Spring '08
 sc
 Math

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