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MATH23X EXIT EXAM REVIEW MATERIAL – DIFFERENTIAL CALCULUS

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MATH23X EXIT EXAM REVIEW MATERIAL – DIFFERENTIAL CALCULUS 1. Find the equation of the tangent line to the curve y = x3 at the point (2,8). 12x – y – 16 = 0 b. x + 12y – 98 = 0 c. 12x + y -98 = 0 d. x – 12y + 16 = 0 2. Find dy/dx in the equationtan〖x+tan〖y=xy〖〖 . a. dy/dx=(y-〖sec〖^2 x)/(〖sec〖^2 y-x) b. dy/dx=(x-〖sec〖^2 y)/(〖sec〖^2 x-y) c. dy/dx=(〖sec〖^2 x-y)/(〖y-sec〖^2 y) d. dy/dx=(〖sec〖^2 y-x)/(〖x-sec〖 3. Compute for the area of the largest rectangle that can be inscribed in the ellipse whose equation is 4x2 + 9 y2 = 36. A.24 B.18 C. 12 D. 9 4. Which of the following functions is continuous for all real numbers? a) f (x) =3x 3 - 4x 2 + 5x - 2 b) x 2 + 3 g(x) = x 2 - 9 c) h(x) = 3x  if 0 ∈ x ∈ 5 if x 5 d) p(x) =tan x 5. Suppose and changes from 3 to 3.1. Find . y(x) =x - 5x + 6 a) 0.01 b) -0.09 c) 0.11 d) 0.17 6. A rectangular box with a square base is to contain 540 cubic inches. If the top costs $0.90 per square inch of material, the bottom $0.40, and the sides $0.20. Find the dimensions of the box so that the cost is minimum. a) $ 104 b) $ 118 c) $ 98 d) $ 127 7. Find the coordinates of the relative extreme points of the function, x 3 f (x) = 3 - . x - 6x 2 a) x =3; x =- 2 b) x =- 3; x =2 c) x =1 / 3; x =- 1 / 2 d) x =- 1 / 3; x =1 / 2 8. An open rectangular box with square base is to be made from 48 ft.2 of material. What dimensions will result in a box with the largest possible volume. a)48 cu.ft. b)32 cu.ft. c)52 cu.ft. d)42 cu.ft. 9. For what values of x is the function f(x)=(x^2-5x+4)/(x^2+3x-4) not continuous? a) 1,4 b)-1, -4 c)1, -4 d)-1, 4 10. Find the derivative with respect to x of y = (2x2 + 6x)(2x3 + 5x2). a) 〖20x〖^4+〖88x〖^3+〖90x〖^2 b) 〖10x〖^4+〖88x〖^3+〖90x〖^2 c) 〖20x〖^4+〖90x〖^3+〖88x〖^2 d) 〖25x〖^4+〖80x〖^3+〖90x〖^2 11. Find the equation of the tangent to the curve y = 3x − x3 at x = 2. a) 9x + 2y - 6 = 0 b)x + y - 16 = 0 c)16x + y - 9 = 0 d)9x + y - 16 = 0 12. An object falling from rest has displacement s in cm given by s = 490t2, where t is in seconds (s).What is the velocity when t = 10 s? a) 4900 cm/s b)9800 cm/s c)980 cm/s d)2450 cm/s 13. Give the slope of the curve 〖y= x/4〖^3- 2x+1 at point (1,1) ............................................................continued....................................................................

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