A runner runs a circular track and a set of data is recorded (time, distance): 68 s, 400 m; 114 s, 600 m; 168 s, 800 m; 209 s, 1,000 m; 256 s, 1,200 m; 322 s, 1,400 m. What is the average velocity from 68 sec to 168 sec?
A3 m/s
B4 m/s
C8 m/s
D6 m/s
Mathematics · Question Bank
Differential Calculus
80 of 112 questions match · page 4 of 4. Answer in your head first, then check the solution.
Water is flowing into a conical vessel 10 ft high and 2 ft in radius at the rate of 50 cu. ft per minute. If the depth of the water is 6 ft, how fast is the radius increasing?
A2.12 ft/min
B12 ft/min
C2.21 ft/min
D11 ft/min
A steel girder 8 m long is moved on rollers along a passageway 4 m wide and into a corridor at right angles with the passageway. Neglecting the width of the girder, how wide must the corridor be?
A3.6 m
B1.4 m
C1.8 m
D2.8 m
A girl is flying a kite which is at a height of 120 ft. The wind is carrying the kite horizontally away from the girl at a speed of 10 ft/sec. How fast must the string be let out when the string is 150 feet long?
A4 ft/s
B5 ft/s
C8 ft/s
D6 ft/s
Find the minimum distance from the point (4, 2) to the parabola \(y^2 = 8x\).
A\(3\sqrt{3}\)
B\(2\sqrt{3}\)
C\(3\sqrt{2}\)
D\(2\sqrt{2}\)
A stone, projected vertically upward with initial velocity 112 ft/sec, moves according to \(s = 112t - 16t^2\), where s is the distance from the starting point. Compute the greatest height reached.
A196 ft
B100 ft
C96 ft
D216 ft
What is the allowable error in measuring the edge of a cube that is intended to hold 8 cu. m, if the error of the computed volume is not to exceed 0.03 cu. m?
A0.002
B0.003
C0.0025
D0.001
Find the value of x for which \(y = 2x^3 - 9x^2 + 12x - 2\) has a maximum value.
A1
B2
C−1
D−2
If f(3) = 7, f′(3) = −2, g(3) = 6 and g′(3) = −10, find \((g/f)'(3)\).
A−82/49
B−49/82
C−49/58
D−58/49
Find the derivative of the function \(y = \dfrac{3}{x^2 + 1}\).
A\(\dfrac{6x}{(x^2 + 1)^2}\)
B\(6x(x^2 + 1)^2\)
C\(\dfrac{-6x}{(x^2 + 1)^2}\)
D\(-6x(x^2 + 1)^2\)
Water is running out of a conical funnel at the rate of 1 cu. in/sec. If the radius of the base of the funnel is 4 in and the altitude is 8 in, find the rate at which the water level is dropping when it is 2 in from the top.
A−1/9π in/sec
B−1/2π in/sec
C1/2π in/sec
D1/9π in/sec
For what value of k will \(x + \dfrac{k}{x}\) have a relative maximum at x = −2?
A−4
B−2
C2
D4
If y = tanh x, find dy/dx.
Asech² x
Bcsch² x
Csinh² x
Dtanh² x
What number exceeds its square by the maximum amount?
A1
B1/2
C1/3
D1/4
Find the derivative of \(x^{-8}\).
A\(-8x^{-9}\)
B\(-8x^{-7}\)
C\(x^{-9}\)
D0
Find the derivative of the function \(y = \dfrac{3}{x^2 + 1}\).
A\(\dfrac{6x}{(x^2 + 1)^2}\)
B\(6x(x^2 + 1)^2\)
C\(\dfrac{-6x}{(x^2 + 1)^2}\)
D\(-6x(x^2 + 1)^2\)
Find the slope of the curve \(y = x + 2x^{-1}\) at (2, 3).
A2
B1/2
C1
D1/4
Find the maximum area of a rectangle which can be inscribed in an ellipse having the equation \(x^2 + 4y^2 = 4\).
A4
B3
C2
D5
Find the height of a right circular cylinder of maximum volume which can be inscribed in a sphere of radius 10 cm.
A11.55 cm
B14.55 cm
C12.55 cm
D18.55 cm
What is the allowable error in measuring the edge of a cube that is intended to hold 8 cu. m, if the error of the computed volume is not to exceed 0.03 cu. m?
A0.002
B0.003
C0.0025
D0.001