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
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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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