Calc Exams 1, 2, and 3

d. 16 cubic feet

A (closed) rectangular box with a square base will be built for $48. The material for the top and bottom of the box costs $2 per square foot, and the material for the sides of the box costs $1 per square foot. What is the volume of the largest box that can be made? a. 32 cubic feet b. 2 cubic feet c. 24 cubic feet d. 16 cubic feet e. 8 cubic feet f. 4 cubic feet

d. 21 feet per second

A bird sits on the ground eating acorns. A second bird is directly east of the first bird, and is flying straight east at a speed of 35 feet per second at a constant height of 20 feet above the ground. How fast is the distance between the two birds increasing when the distance is 25 feet? a. 20 feet per second b. 19 feet per second c. 17 feet per second d. 21 feet per second e. 16 feet per second f. 18 feet per second

e. 6.25

A circular sector with radius (r) and an angle of θ in radians as show below has an enclosed area of A=1/2r²θ. The length of the circular arc is rθ. What is the maximum possible area if the perimeter of such circular sector is 10? a. 30125 b. 10.5 c. 8.25 d. 12.5 e. 6.25 f. 2.5

c.-32

A diver in midair has vertical position given by h(t)=−16t²+5t+25 where h(t) is the diver's height above the water, in feet, t seconds after beginning the dive. What is the diver's acceleration, in ft/sec², t seconds after the dive begins? a. -28t b. -16 c.-32 d.-32t+5 e. 25 f.-28t+25

a. 27 radios per hour

A worker who works at a factory for x hours will assemble R radios, where R(x) =-x³+6x²+15x for 0≤x≤5. At what rate is the worker assembling radios when x=2? a. 27 radios per hour b. 3 radios per hour c. 12 radios per hour d. 0 radios per hour e. 46 radios per hour f. 23 radios per hour

d. All of them

Consider the function: f(x)=(x²+2x+1)/(3x-9) Consider the following statements: I. f does not have a horizontal asymptote II. f has a vertical asymptote at x=3 III. The x-intercept of f is (-1,0) Which of these statements is/are TRUE? a. II. only b. III. only c. I. only d. All of them e. I and III only f. I and II only

b. cot(x)-csc(x)+C

Evaluate the indefinite integral ∫csc(x)(cot(x)-csc(x))dx a. csc(x)-cot(x)+C b. cot(x)-csc(x)+C c. cot(x)csc(x)+C d. 2cot(x)csc(x)+C e. cot(x)+csc(x)+C f. -cot(x)-csc(x)+C

d. 19/64

Find f'(4), given f(x)=(x²-1)/(√x³) a. 11/64 b. 7/6 c. 2/3 d. 19/64 e. 7/8 f. 109/64

a.-2sinx+1/2x²+3x

Find f(x) if f''(x)= 2sin(x)+1 f'(0)=1 f(0)=0 a.-2sinx+1/2x²+3x b. -2sinx+x²+3x c. 2sinx+1/2x²+x d. 2sinx+1/2x²+3x e. -2sinx +1/2x²+3x-1 f. 2sinx+1/2x²+x-1

a. -3sin(3x)sec²(cos(3x))

Find f′(x) given that f(x)=tan(cos(3x)). a. -3sin(3x)sec²(cos(3x)) b. sec²(cos(3x))+3cos(3x) c. cos(3x)-3sec²(sin(3x)) d. 3sin(cos(3x)) e. -sec²(3sin(3x)) f.-3cot(3x)

1/6

Find the Limit: lim as x→3 of (x-2)³/ (x+3) a. DNE b. ∞ c. -∞ d. 1/2 e. 1/6 f. 1/9

c. 0 and -1

Find the critical number(s) of y=3x²e^(2x) a. 0 and 1 b. -1 only c. 0 and -1 d. -1 and 1 e. 1 only f. 0 only

c. (-10x)/(√r²-10x²)

Find the derivative of y=√r²−10x², where r is a constant. a. (r²-10x²)/(√2r-20x) b. (-10x²)/(√2r-20x) c. (-10x)/(√r²-10x²) d. (r-10x)/(√r²-10x²) e. (r²-10x²)/(2√r²-10x²) f. 10/√r²-10x²

d. y=-x+π+3

Find the equation of the tangent line to the graph of g(x)=3+sin(x) at x=π a. y=x-π+3 b. y=2x-2π-3 c. y=x-π-3 d. y=-x+π+3 e. y= -x-π+3 f. y=2x-2π+3

c. (-1/2,3)

Find the largest open interval where f(x) = 1/6x⁴-5/6x³-3/2x²+2x+5 is concave downward. a. (0,3) b. (0,∞) c. (-1/2,3) d. (-∞,-1/2) e. (3,∞) f. (-2,3)

e. (0,5)

Find the largest open interval where h(t) is decreasing. h(t)=t³-15/2(t²) a. (0,15/2) b. (-∞,5) c. (5,∞) d. (-∞,0) e. (0,5) f. (15/2,∞)

e. y=3x+5

Find the slant asymptote of h(x) = (3x³+11x²+16x+9)/(x²+2x+1) a. y=11x+4 b. y=2x+1 c. y=11x d. y=3x e. y=3x+5 f. y=2x+11

a. -1

Find the x value at which g(x)=xe∧x has a horizontal tangent line. a. -1 b.1 c.2 d.1/2 e.-2 f.0

d. 4

Find the x-coordinate of the absolute maximum of g(x) = x³-3x²+12 on the closed interval [-2,4]. a. 3 b. -2 c. 2 d. 4 e. 1 f. 0

f. -1/5

Find the x-coordinate of the point on the graph of f(x)=2x+4 that is the closest to the point (1,3). a. 18/5 b. -3/5 c. -18/5 d. 3/5 e. 1/5 f. -1/5

c. 3sec(x)tan²(x)+3sec³(x)

Given f(x)=3sec(x)tan(x). Find f′(x). a. 3sec²(x)tan(x)+3sec(x) b. 3sec³(x)tan(x) c. 3sec(x)tan²(x)+3sec³(x) d. 3sec(x)tan(x)+3sec²(x) e. 3sec(x) f. 3sec(x)tan²(x)-3sec³(x)

15x²−8/3x∧1/3−6/x³

Given f(x)=5x³−2x^(4/3)+3/x². Find f′(x). a. 15x²−8/3x∧1/3−6/x b. 15x²−8/3x∧1/3−6/x³ c. 3x²−4/3x∧1/3−3/x³ d. 3x²−8x∧1/3−6/x e. 15x²−8/3x+6/x³ f. 15x²−8/3x∧1/3+6/x³

e. relative maximum: (−1,2); relative minimum: (1,−2)

Given f(x)=x³−3x, find the relative extrema. a. relative maximum: (1,−2); relative minimum: (−1,2) b. relative maximum: (−1,1); relative minimum: (−2,2) c. relative maximum: (−2,1); relative minimum: (2,−1) d. relative maximum: (2,−1); relative minimum: (−2,1) e. relative maximum: (−1,2); relative minimum: (1,−2) f. relative maximum: (3,−1); relative minimum: (−1,3)

c. -3.1774

Given yln(x)=xln(y), use implicit differentiation to find dy/dx at the point of (2,4). (Round to 4 decimal places.) a. -9.6251 b. 2.0422 c. -3.1774 d. -5.2755 e. 0.8448 f. -2.7204

a. 8e^(2t)+8cos(2t)

If f(t)=e^(2t)−sin(2t), find the 3rd derivative, f³(t). a. 8e^(2t)+8cos(2t) b. 8e^(2t)+8sin(2t) c. 8e^(2t)-8cos(2t) d. 2e^(2t)+2cos(2t) e. e^(2t)-cos(2t) f. e^(2t)+sin(2t)

e. ⁵√x²+1

The derivative of a function is found by computing f'(x)= lim as h→0 (5√(x+h)² +1)-(5√(x²+1))/h Which of the following could be f(x)? a. ⁵√x² b. (x+h)²+1 c. 1/(⁵√x²) d. x²+1 e. ⁵√x²+1 f. ⁵√(x+h)²+1

d. -2 only

The graph of f'(x) is given. Find the x-value of any inflection point(s) of f(x). a. -4 only b. 0 only c. 4 only d. -2 only e. -4 and 0 only f. -4, -2 and 0 only

c. 13 feet

The position of a particle moving in a straight line is given by s(t)=7/3t³−7t²−t+16 where t is in seconds and s(t) is in feet. What is the particle's position when its velocity is 20 ft/s? a. 20 ft b.0 ft c.13 ft d.16 ft e.5 ft f.9 ft

d. 48π

The radius of a sphere changes at a rate of 2 inches per second. What is the rate of change of the surface area of the sphere, in in²/sec, when the radius is 3 inches? The surface area of the sphere is given by the formula S=4πr² a. 72π b.108π c. 24π d. 48π e. 16π f. 36π

f. (4x³-y)/(3y²+x)

Use implicit differentiation to find dy/dx given y³+xy=x⁴. a. (4x³)/(3y²-x) b. (4x³-y)/(3y) c. (4x³-y-x)/(3y²) d. (4x³-3y²)/(x) e. (4x³-3y²-y)/(x) f. (4x³-y)/(3y²+x)

e. 11/7

What is the slope of the tangent line to the graph of y=ln(2x³+5x) at x=1? a. 1/2 b. 1/7 c. 7/11 d. ln7 e. 11/7 f. 77

e. (x²-16)/(x-4)

Which of the following functions has a hole at x=4? a. (x+4)/(x²-16) b. (x+4)/(x-4) c. x-4 d. x/(4-x) e.(x²-16)/(x-4) f. 1/(x-4)

d. I only

Which of the following is/are true? I. lim as x→∞ of (-12x⁸+4x²)/(6x⁵+6) = -∞ II. lim as x→∞ of (10x³+100x+1000)/(-5x³+x²+x+1) = -1/2 III. lim as x→∞ of (14x⁶+3)/(x⁷+x⁹) = 14 a. I and III only b. III only c. II only d. I only e. I, II and III f. II and III only

a. 6x^(2/3)-2ln|x|+C

∫(4 ³√x² -2)/(x) dx = a. 6x^(2/3)-2ln|x|+C b. 9x^(3/2)-2ln|x| +C c. 9x^(3/2) -2+C d. 6x^(2/3)-2+C e. 6x^(1/2) - 2/(x²) +C f. -4/3x^(-4/3) +2/(x²) +C