Calc Midterm 3

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Rutgers University *

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151

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Mathematics

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Jan 9, 2024

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RUTGERS UNIV. OFFICIAL MATH 151 MIDTERM QUIZ © 2020 Suppose that the functions f and g and their derivatives with respect to x satisfy the following: f(1)=0,f(2)= -7,'(1)=7,1'(2)=3, 9(1)=3,9(2)=2,9'(1)=3,9'(2)=5 Rutgers Quiz (ver. a162t) © 2020 For each of the following functions, compute the desired derivatives. Your answers do not need to be simplified. (a) For the function F(x)= e 9x= 1)g(x), the value of F'(1)= 9+3+ 3. Rutgers Quiz (ver. a162t) © 2020 N (b) For the function G(x) SIN0) e value of G 1) ! or the tunction X)=—"7- , the value 0 =3 g(x) 3 Rutgers Quiz (ver. a162t) © 2020 _ ) 20343423 (c) For the function H(x)= In ([g(x)]? +f(2 x)), the value of H '(1)= ST Rutgers Quiz (ver. a162t) © 2020 RUTGERS UNIV. OFFICIAL MATH 151 MIDTERM QUIZ © 2020 Question is complete. Tap on the red indicators to see incorrect answers.
RUTGERS UNIV. OFFICIAL MATH 151 MIDTERM QUIZ © 2020 Find the x-coordinate(s) of the point(s) on the curve y = X3 +4x% - 2x + 19 where the tangent line is parallel to the line y = 7x + 15. (If you find more than one x-coordinate, separate the numbers by commas.) Rutgers Quiz (ver. e745t) © 2020 N 5 The x-coordinate(s) is/are: - 30 1 RUTGERS UNIV. OFFICIAL MATH 151 MIDTERM QUIZ © 2020 Question is complete. Tap on the red indicators to see incorrect answers.
RUTGERS UNIV. OFFICIAL MIDTERM QUIZ © 2020 Suppose f(x)=b* and f'(0)=16. Find b. b=e*. Rutgers Quiz (vers. d469r) RUTGERS UNIV. OFFICIAL MIDTERM QUIZ © 2020 Question is complete.
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RUTGERS UNIV. OFFICIAL MIDTERM QUIZ © 2020 Consider the curve with equation 2x e ¥ + sin ~ 1 (5y)=2. Rutgers Quiz (ver. e898r) d (a) Use implicit differentiation to find _y_ Your answer does not need to be simplified. dx dy 24/1-25y eV X f1-252 V45 Rutgers Quiz (ver. e898r) (b) Find an equation of the tangent line to the curve at the point (1,0). Put the equation for the tangent line in the box. - .2_ 1 y=-Z(x-1) Rutgers Quiz (ver. e898r) RUTGERS UNIV. OFFICIAL MIDTERM QUIZ © 2020 Question is complete.
RUTGERS UNIV. OFFICIAL MATH 151 MIDTERM QUIZ © 2020 Water is flowing into a conical tank with base radius 9 ft and height 54 ft. The tank is oriented so the the tip of the cone is pointed downward. Recall that the volume V of a right circular cone is given by 1 V=3 ?h, where r is the base radius of the cone and h is the height of the cone. Use this information in parts (a) and (b). Rutgers Quiz (vers. d217p) © 2020 Rutgers Quiz (vers. d217p) © 2020 (a) Find a formula for the volume V of the water in the tank as a function of h only, where h represents the depth of the water in the tank. You do not need to simplify your answer. Al Ve ta 2 2h3 = 3" 54 i (b) If water is flowing into the tank at a rate of 14 cubic feet per minute, how fast is the depth of the water changing when the depth is 45 feet? Give an exact answer and NOT a decimal approximation. You do not need to simplify your answer. Rutgers Quiz (vers. d217p) © 2020 hl 2.14 3, . > ft*/min. The depth of the water is changing at a rate of 2 ne9” «45 RUTGERS UNIV. OFFICIAL MATH 151 MIDTERM QUIZ © 2020 Question is complete. Tap on the red indicators to see incorrect answers. @
RUTGERS UNIV. OFFICIAL MATH 151 MIDTERM © 2020 Fill in the blanks. The figure below shows the velocity v = f(t) of a particle moving on a horizontal coordinate line for the time interval 0 < t < 10 seconds. Rutgers Quiz (ver. c818r) © 2020 Velocity as a Function of Time Vv Q 6_ 44 = 29 o \ /\‘ 0 T T Y 4 6 8 10 24 -4 -6~ Rutgers Quiz (ver. c818r) © 2020 Question is complete. Tap on the red indicators to see incorrect answers. Answer the following questions concerning the movement of the particle. For each answer, type an equation or a compound inequality, using t as the variable. Use a comma to separate answers as needed. The inequalities and solutions, if there are multiple, should be ordered from left to right. Rutgers Quiz (ver. c818r) © 2020 (a) When is the particle moving to the right? 0<t<1,8<t<10 (b) When is the particle stationary for more than an instant? 1<t<?2 Rutgers Quiz (ver. c818r) © 2020 (c) When is the particle moving at its greatest speed? 4<t<6 (d) When is the particle's acceleration positive? 6<t<g Rutgers Quiz (ver. c818r) © 2020
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