Version 001 Exam Review Practice Problems NOT FOR A GRADE alexander (55715) 1
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1 Version 001 Eam Review Practice Problems NOT FOR A GRADE aleander This print-out should have 7 questions. Multiple-choice questions may continue on the net column or page find all choices before answering. CalCi17s points At noon, ship A is 0 milesdue west of ship B. ShipAissailingsouthat5mphwhileship B is sailing north at 15 mph. At what speed is the distance between the ships changing at :00 pm? speed = 1 mph. speed = 1 mph speed = 15 mph speed = 16 mph speed = 1 mph CalCi08a points The dimensions of a cylinder are changing, but the height isalwaysequal to thediameter of the base of the cylinder. If the height is increasing at a speed of 5 inches per second, determine the speed at which the volume, V, is increasingin cubic inches per second when the height is inches.. dv dt dv dt dv dt dv dt dv dt = 1π cub. ins./sec = 1π cub. ins./sec = 1π cub. ins./sec = 16π cub. ins./sec = 15π cub. ins./sec CalCi0a points A circle of radius r has area A and circumference C are given respectively by A = πr, C = πr. If r varies with time t, for what value of r is the rate of change of A with respect to t half the rate of change of C with respect to t? r = 1. r = π r = 1 r = π r = r = π CalCia points A balloon is released 6 feet away from an observer. The balloon is rising vertically at a rate of ft/sec and at the same time the wind is carrying it horizontally away from the observeratarateofft/sec. Atwhatspeedis the angle of inclination of the observer s line of sight changing seconds after the balloon is released? speed = 6 1 rads/sec. speed = 1 8 rads/sec speed = 15 8 rads/sec speed = 11 8 rads/sec speed = 7 1 rads/sec
2 Version 001 Eam Review Practice Problems NOT FOR A GRADE aleander CalCi15s points The height of a triangle is increasing at a rate of cm/min while its area is increasing at a rate of 1 sq. cms/min. At what speed is the base of the triangle changing when the height of the triangle is cms and its area is 1 sq. cms? speed = 8 cms/min. speed = 0 cms/min speed = cms/min speed = cms/min speed = 7 cms/min CalCi08b points If the radius of a melting snowball decreases at a rate of ins/min, find the rate at which the volume is decreasing when the snowball has diameter inches. rate = 8π cu.ins/min. rate = 9π cu.ins/min rate = 7π cu.ins/min rate = 6π cu.ins/min rate = 0π cu.ins/min CalCi06b points A point is moving on the graph of When the point is at 5 +6y = y. P = 1 11, 1 11, its y-coordinate is increasing at a speed of units per second. What is the speed of the -coordinate at that time and in which direction is the - coordinate moving? speed = 19 units/sec, decreasing. speed = 9 units/sec, decreasing speed = 9 units/sec, increasing speed = 1 speed = 19 speed = 1 units/sec, decreasing units/sec, increasing units/sec, increasing 7. speed = 5 units/sec, increasing 8. speed = 5 units/sec, decreasing CalCi09s points A street light is on top of a 1 foot pole. A person who is feet tall walks away from the pole at a rate of 6 feet per second. At what speed is the length of the person s shadow growing? speed = 5 ft/sec. speed = 1 8 ft/sec speed = ft/sec speed = 11 ft/sec speed = 8 ft/sec
3 Version 001 Eam Review Practice Problems NOT FOR A GRADE aleander CalCi0s points Determinethevalueof/dtat = when and d/dt =. = 1 dt = = 5 dt = = 7 dt = = 9 dt = = dt = y = 5 CalCi0s points Arockisthrownintoastillpondandcauses a circular ripple. If the radius of the ripple is increasing at a rate of 6 ft/sec, at what speed is the area of the ripple increasing when its radius is 5 feet? speed = 60 sq. ft/sec. speed = 6π sq. ft/sec speed = 61 sq. ft/sec speed = 6 sq. ft/sec speed = 60π sq. ft/sec speed = 6 sq. ft/sec 7. speed = 6π sq. ft/sec 8. speed = 61π sq. ft/sec CalCi7s points Boyle s Law states that when a sample of gas is compressed at a constant temperature, the pressure and volume satisfy the equation PV = C,whereC isaconstant. Supposethat at a certain instant the volume is 00 ccs, the pressure is 60 kpa, and the pressure is increasing at a rate of 6 kpa/min. At what rate is the volume decreasing at this instant? rate = 18 ccs/min. rate = 0 ccs/min rate = 1 ccs/min rate = 16 ccs/min rate = 1 ccs/min CalCi06c 01 part 1 of 10.0 points A point is moving on the graph of When the point is at +y = y. P = 1 5, 1 5, its -coordinate is decreasing at a speed of units per second. What is the speed of the y-coordinate at that time? speed y-coord = units/sec. speed y-coord = 1 units/sec speed y-coord = units/sec speed y-coord = 7 units/sec speed y-coord = 7 units/sec
4 Version 001 Eam Review Practice Problems NOT FOR A GRADE aleander part of 10.0 points In which direction is the y-coordinate moving at that time? direction decreasing y. direction increasing y d = sec y sec y d = sec y sec y+ CalCg1eam points CalCi00E points A 5 foot ladder is leaning against a wall. If the foot of the ladder is sliding away from the wall at a rate of 9 ft/sec, at what speed is the top of the ladder falling when the foot of the ladder is feet away from the base of the wall? speed = 7 ft/sec. speed = 8 ft/sec speed = 5 ft/sec speed = 1 ft/sec speed = 1 ft/sec CalCg06b points Find d when tan y = y. Determine /d when. y cos = d = y cos d = y tan d = y sin d = y cot d = y cot d = y tan Find d when CalCg08a points tany = +y. d = +sec y sec y d = sec y ysec y+. d = sec y sec y. d = +sec y ysec y+ d = sec y+ sec y d = ysec y sec y+ d = sec y sec y+ d = +ysec y sec y
5 Version 001 Eam Review Practice Problems NOT FOR A GRADE aleander d = ysec y sec y f = 5 5 d = sec y ysec y CalCg05d points Find /d when. d = y d = 5 y d = 5 y d = y d = 5y d = 5 y CalCg0a points 5 +y = CalC7e5a points Find d when. +y 9y 1 = 0. d = y y + d = +y y d = y y d d = y y = y + y + Find /d when CalCg0b points y = 6 y. Determine f when f = tan 1. 5 d = y + 6+ y Hint : first simplify f. f = +5. y d = 1 +1 y. f = f = f = y d = 1 1 y d = y 6 y
6 Version 001 Eam Review Practice Problems NOT FOR A GRADE aleander d = y 6+ y y d = y CalC7eb points f = f = CalC7ea points Find the derivative of f = sin 1 e. Find the derivative of f = f = 1 sin 1. sin 1. f = 1 cos sin f = cos sin f = f = f = 1 sin 1 sin 1 1 sin 1 CalC7e5b points Determine f when f = sin 1. + Hint : first simplify f. f = +. f = + f = + f =. f = f = f = f = f = 1+e 6 1 e 6 1+e e 1 e 1 e 6e 1 e 7. f = 6e 1+e 8. f = e 1+e CalCg5c points The points P and Q on the graph of y y 5y +10 = 0 have the same -coordinate =. Find the point of intersection of the tangent lines to the graph at P and Q. 5 intersect at = 7, intersect at = 7, 0 7
7 Version 001 Eam Review Practice Problems NOT FOR A GRADE aleander intersect at = intersect at = intersect at = Find y when y = 5+ y. y = y , , 5 5, 0 7 CalCg01a points y +5+ = y = y +5+6 y = y +5+6 y = y +5+ y = y +5+ CalC7e1a points Determine the derivative of f = arcsin. f = f = 9 9 CalC7b50a points If y = y is defined implicitly by 7e y = y +7, find the value of /d at, y = 1, 0.. d = 7 18 d = 9 d = 7 d = 1 d = 7 18 d = 7 CalCg0a points Find d when y = f = 1 d = 1 5 y1/. f = 6 9. d = 5y1/ f = 1 d = 1 / 5 y f = 6 1 y / d = 5
8 Version 001 Eam Review Practice Problems NOT FOR A GRADE aleander / d 5 = 1 y y / d = 5 L = 1 1 L = CalC7ea points Find the derivative of f = 1. arctan f 1 = 1+ arctan. f 1 = + arctan f = 1 sec tan f = + arctan f = 1+ arctan f = sec tan CalCj06s points Find the linearization of at = 0. f = 1 1 L = 1. L = L = L = CalCj09s points Use linear approimation with a = to estimate the number as a fraction CalCjs points Use linear appproimation to estimate the value of 15 1/. Hint: 16 1/ =. 15 1/ / 15 1/ / / 1 16 CalCc6s points Find the derivative of f when f = +.
9 Version 001 Eam Review Practice Problems NOT FOR A GRADE aleander f = +. f = f = + f = + f = f = CalCc0a points Find the y-intercept of the tangent line at the point P,f on the graph of f = ++ f = 1 1 f 1 = 1 f = 1 CalCa10s points Find an equation for the tangent to the graph of f at the point P, f when f = y = y = 0 y = y-intercept = 11. y-intercept = 11 y-intercept = 1 y-intercept = 1 y-intercept = y-intercept = Find f when f = CalCc7s points f = f = 1 1 y = y = 7 CalCc7b points Find the derivative of + g = g = g = + +1 g = g = g = +1
10 Version 001 Eam Review Practice Problems NOT FOR A GRADE aleander g = +1 CalCc0a points Let f, g be differentiable functions. Consider the following statements: A. If F 1 = {f 1/f}, then { F 1 = f f+ 1 } f. B. If F = fg, then F = f g fg. C. If F = f/g, then F = f g+fg g. Which of these statements are true? all of them. B and C only f a = a+. f a = a+ f a = a+ f 1 a = a+ f a = 1 a+ f a = 1 a+ CalCe1a points Find the derivative of f when f = tan +8sec. f = +8cos cos+8 B only. f = sec +8sectan A only C only A and B only 7. none of them 8. A and C only CalCa15s points Find the value of f a when ft = t+7 t+. f sec = +8sectan f = sin+8cos cos+8 f = sec+8 +8sec f = cos+8 cos+8 CalCd101b points Determine f when f = sin 1 sin+.
11 Version 001 Eam Review Practice Problems NOT FOR A GRADE aleander f = 5cos sin+. f = 5cos sin+ f = sincos sin+ f = 5sincos sin+ f = cos sin+ f = cos sin+ CalCe101b points Find the derivative of f = 1 cos sin f = +cos sin. f = 1 sin cos f = +cos sin f = cos sin f = 1+sin cos f = 1 sin cos CalCe6a points Find anequationfor thetangent linetothe graph of f = 1 sec+cos. at the point 1 π, f1 π. y = 1 π. y + = π 1 y = 1 π y = 1 π y = 1 π y + = π 1 CalCe0s points Find the derivative of g when g = cos. g = sin cos. g = sin cos g = cos sin g = sin+cos g = cos+sin g = cos sin CalCe1s points Find anequationfor thetangent linetothe π π graph of f at the point P, f when f = 7tan. y = π
12 Version 001 Eam Review Practice Problems NOT FOR A GRADE aleander y = π y = +9 1 π y = π y = π CalCe05a points Find the derivative of f = sin+cos. f = + sin. f = cos f = sin f = sin f = +cos f = cos
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