24. the radius of a right circular cylinder of height 10cm increases at a rate of 3cm/min What is the rate of change of the volume of cylinder when the radius is 8cm? A. 80pi cm^3/min B 320pi cm^3/min C 480pi cm^3/min D 640pi cm^3/min 25 int (x^2-1)/(x^3)+x dx=underline ( ) A. lnvert x^2+1vert +lnvert xvert +C C. lnvert x^2+1vert -lnvert xvert +C B 1/2lnvert x^2+1vert -lnvert xvert +CD.2lnvert x^2+1vert -lnvert xvert +C 26. the area of the region bounded between the graph of y=x^2 and y=sqrt (x) is B. A. 35 1/3 C. 2/3 D. 1 27. What is the area of the region between the graph of y=x^2 and y=-x+2 for 0leqslant xleqslant 2 A. 3 B. 2 C. 3/2 D. 2/3 28. If f(x)=(x+1)/(x-1) and f(a)=5 , then f(2a)=underline ( ) A. 2 B. 4 C. 6 D. 8 29. Which one of the ff is the set of all critical numbers of f(x)=(x^3)/(3)-vert 4x-1vert A. (1)/(4),2 B -2,(1)/(4),2 C. -2,2 D. (1)/(4) 30. If a box with square base and open top is made from 1200cm^2 material, what is the largest volume of the box in cm^3? A. 4000 B. 8000 C. 15000 D. 3000 31. Which one of the ff is true about the function f defined by f(x)=x^2+e^2x A. fis decreasing for xgeqslant 0 C. f has relative minimum at x=0 B. fis increasing for xgeqslant 0 D. fhas relative maximum at x=0 32. given f(x)= ) x+1 cospi x for xlt 0 A. (1)/(2)+(1)/(pi ) B. (1)/(2)-(1)/(pi ) C (1)/(2) D. (-1)/(2) 33. If 2leqslant f'(x)leqslant 4 for all values of x,then the value of f(8)-f(2) is between which of the ff numbers? A. 14 and 24 B. 12 and 24 D. 8 and 10 C. 12 and 18 34. Which one of the ff is a convergent sequence? A. ((-1)^n)/(4) B. (4+3^n)/(5^n) C. (2-5^n)/(3^n) 35. What is the maximum value of the function f(x)=x^4-2x^2 on [-2,1] A. 40 B. 12 C. 24 D. 8 36. What is the slope of the tangent line to the graph of f(x)=3x^3+sqrt (x)+2at(1,6) A. (19)/(2) B. (17)/(5) C. (13)/(2) D. 6 37. What is the partial fraction decomposition of (x^2+x+1)/((x+2)(x^2)+1) A. (2)/(3(x+2))+(2x+1)/(3(x^2)+1) C. (2)/(5(x+2))+(3x+1)/(5(x^2)+1) B. (5)/(3(x+1))+(2x+1)/(3(x^2)+1) D. (3)/(5(x+2))+ 38. let f(x)=(3x+1)/(x-2) then what is the range of f(x) A. Rvert 3 B. R C. Rvert (-1)/(3) D. Rvert 3 39. Let f(x)=x-x^2 and g(x)=(1)/(x') then what is g(f((1)/(x))) A. x-x^2 B (1)/(x^2-x) C. (x^2)/(x-1) D. (x-1)/(x^2) 40.Let A_(n) be arithmetic sequence with ngeqslant 1 ,where a_(1)=3 and a_(n+1)=a_(n)+2 then a_(4)+a_(5)+a_(6)+ldots ldots ldots ..+a_(29)=underline ( ) A. 122 B.546 C.884 D.909 41.The sum of the first three geometric sequence is 16 and the sum the next three geometric sequence is 128 .Then what is the common ratio? A. 3 B.2 C.1 D. 7 42. Which of the following function is differentiable at a point? 43.The sum of the first 8 terms of arithmetic sequence is 104 and the sum of the next 12 terms is 636,then what is their common difference? A. 10 B. 12 C.15 D. 20 44. Let f(x)=Sgn(6-n) where n=1,2,3,ldots ldots ,th ,the function? A.6 B.5 C.4 different terms can obtain from the given