Download 40 Multiple Choice Questions on Calculus I - Final Examination | MATH 251 and more Exams Calculus in PDF only on Docsity!
- The value of x -^25 3 x - 13 x- 10 2 2 x 5
lim is:
a) 0 b) 1 c) 3 d) 1. e) not defined
2. The value of
x
5 sin x
lim x - is: a) 1 b) 5 c) undefined d) - e) 0
- The function y = f(x) has a nonremovable (jump) discontinuity at x = a if a) limf(x)^3 x a and f(a) = 5 b) lim f(x)^3 x a and lim f(x)^5 x a c) lim f(x^ ) x a and lim f(x^ ) x a d) lim f(x)^3 x a and lim f(x^ ) x a
e) limf(x)^3 x a and f(a) = 3
a) -sin x b) -cos x c) sin x d) cos x e) 0
- The equation of the line tangent to the graph of f(x)^ =^15 - x at the point (11, 2) is a) 4 19 x 4 1 y b) 4 11 x 4 1 y c) 4 1 y d) 4 11 x 4 1 y e) 4 3 x 4 1 y
- The derivative of f(x) = (2x^3 + x + 5)^4 is: a) 4 (6x^3 + 1)^3 b) 5 1 (6x^3 + 1)^5 c) 5 1 (2x^3 + x + 5)^5 d) 4 (2x^3 + x + 5)^3 (6x^2 + 1 + 5) e) 4 (2x^3 + x + 5)^3 (6x^2 + 1)
- The graph of the first derivative of a function is shown below:
Which of the following graphs could be the graph of the original function? a) d) b) e) c)
a) (^2) y 3 x dx dy b) x 2 x 2 y dx dy c) 2 y x 2 x y dx dy d) 2 y x 2 x dx dy e) 2 y x 2 x y dx dy
- The absolute maximum value of f(x) = (x + 2) 2 (19 - x) over the interval [-6, 0] is: a) 72 b) 76 c) 400 d) 1372 e) 40572
- Let f(x) = x 1 x (^2) . The number of inflection points of the graph of f(x) is: a) none b) one c) two d) three e) four
- A rancher has 1600 feet of fencing in which to enclose three corrals as shown in the diagram. What dimensions (rounded to the nearest hundredth) should the corrals have in order to enclose the maximum area? x y y 3 2
a) x = 266.67 feet y = 266.67 feet b) x = 266.67 feet y = 300 feet c) x = 300 feet y = 262.5 feet d) x = 262.50 feet y = 300 feet e) x = 200 feet y = 375 feet
- A hot air balloon is floating at a constant altitude of 400 feet when it passes over a small child. The wind is blowing east at a rate of 15 feet per second. How fast (rounded to two decimal places) is the distance between the child and the balloon increasing after 10 seconds? a) 5.27 feet per second b) 26.67 feet per second c) 15.00 feet per second d) 427.20 feet per second e) 28.48 feet per second
- Estimate the area under the curve y = x^3 + x on the interval [1, 3] with n = 4 subintervals using the midpoint of each subinterval. a) 35 b) 47.5 c) 65 d) 80.5 e) 23.
- Find t -^1 dt dx d 2 x 2. a) x - 1 1 2
c) 12a^3 – 6a^2 – 6 d) 4a^3 – 3a^2 – 1 e) 4a^3 – 3a^2 + 4a + 5
- Find (^) x (x^2 + 3 )^16 dx. a) 3 x +C 3 x x 2 1 3 16 2 b) (^) x(x+^3 )+C 34 (^1 ) c) (^) C 17 3 x 49 x 49 17 d) (^) (x 3 ) +C 34 (^1 2 ) e) (x+^3 x) +C 17 (^1 )
- Find ^ 3 1 2 dx 1 3 x x . a) 7 1 b) ^71 3 2 c) 0 d) 7 e) Does not exist
- The velocity of an object at any time t (in seconds) is given by: v(t) = t^2 + cos t. Initially, the object is at position s = 10 feet. What is the object’s position (rounded to two decimal places) 8 seconds later? a) 171. b) 169. c) 175. d) 179. e) 181. Problems 24-26 refer to the figure which is the graph of y x^2 4 x 2 and y^ ^ ^3 x^8.
b) (^) 6 1 ( x^2 7 x 7 )^2 dx c) (^) 6 1 ( x^2 7 x 6 )^2 dx d) (^) 6 1 [ ( x^2 4 x 15 )^2 ( 3 x 21 )^2 ]dx e) (^) 6 1 [ ( x^2 4 x 11 )^2 ( 3 x 5 )^2 ]dx
- Find the average value of the function f (x) 6 x^2 4 x 1 on the interval [0,5]. a) 2 131 b) 75 c) 5 d) 205 e) 41
- A rectangular tank with base 3 feet by 8 feet and height 12 feet is full of water. Find the work required to pump the water to a point 5 feet above the top of the tank. Assume the density of water is 62.5 lb/ft^3. a) 8250 ft-lbs b) 198000 ft-lbs c) 108000 ft-lbs d) 89250 ft-lbs e) 216750 ft-lbs
- Find the derivative of f(x) = sinh x tanh x. a) f ' (x) = sinh x sech^2 x + tanh x cosh^2 x b) f ' (x) = sinh x sech 2 x + tanh x c) f ' (x) = sinh x sech^2 x + tanh x cosh x d) f ' (x) = sinh x sech x + tanh x cosh x e) f ' (x) = sinh x sech x + tanh x cosh^2 x
30. Define f(x) =
x t dt 1 for x > 0. Which of the following is not true a) dx x df ( x ) 1 b) f(x) is an increasing function c) f(x) is a one to one function d) f(1) = 0
e) f(x) 0 for all x
- Find the area of the surface obtained by rotating the curve y = 2x over the interval [0,1] about the y-axis.
a)
5 6
b) 5
No longer in Math 251,
c) 2 ^5 this is now in Math 252
d) ^5 So not on your final.
e) 5
- Find the points on the curve y = 2x^3 + 3x^2 – 36x + 3 where the tangent line is horizontal. a) (-2, 71) and (2, -41) d) (-3, 84) and (3, -24) b) (-3, 84) and (2, -41) e) (-2, 71) and (3, -24) c) (-2, 71), (2, -41), (-3, 84), and (3, -24)
- Differentiate the function: f(t) = ln (cos (6t)). a) f ' (t) = cos( 6 t) 6 d) f ' (t) = cos( 6 t) 1 b) f ' (t) = -6 cot (6t) e) f ' (t) = -6 tan (6t) e) f ' (t) = 6 sec (6t)
- At noon, ship A is 160 km west of ship B. Ship A is sailing south at 32 km/hr and ship B is sailing north at 30 km/h. How fast is the distance between the ships changing at 4:00 p.m.? Round the result to the nearest thousandth if necessary. a) 52.099 km/h d) 52.098 km/h b) 52.208 km/h e) 52.096 km/h c) 52.048 km/h
- Use Newton's Method with the initial approximation x 1 = 10 to find x 4 , the fourth approximation to the root of the equation: x^3 + x^2 – 6 = 0. a) x 4 = 6.09191 d) x 4 = 4. b) x 4 = 2.88191 e) x 4 = 1. c) x 4 = 1.
- Differentiate the function: f(t) = t 9 3 t (^). a) f'(t) = 2 5 t t 9 t d) f'(t) = 2 t t 11 2 t 1 b) f'(t) = 2 t t 11 2 3 t (^) e) f'(t) = 2 t t 9 2 t 3 c) f'(t) = 2 t t 9 t 3
