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Impl-dif-tut-que

# Impl-dif-tut-que - 7 Find y if 3 x 2 7 y 2 = 8 7 1 8 Find y...

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ECON 331 Tutorial Questions Topic: Implicit Differentiation and Chain Rule Note: Where necessary, rewrite funtions into the form: F(x,y,z)=0 and use implicit function Theoem. For Multiple choice, SHOW your work MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) If z = x 3 y 2 + x 2 y 3 - 3 xy and x = 2 r + 3 s and y = r - s , then z s when r = 1 and s = 0 is A) 35. B) 17. C) 8. D) 5. E) 1. 1) 2) If z = (2 x + 3 y ) 3 and x = r 2 - 2 s and y = 2 s - r , then z s when r = 2 and s = 1 is A) 88. B) 104. C) 84. D) 96. E) 92. 2) 3) If x 2 + xy + yz + z 2 = 6, then z y = A) - x + z 2 z B) - x + 2 z x + 2 y C) - x + 2 z y D) - y + 3 z y E) - x + z y + 2 z 3) 4) If s 3 t 3 + 2 r 2 - s 2 = 1, then t r = A) - 4 r 3 s 3 t 2 . B) r - 3 s 2 t . C) 4 r. D) 3 1 - 2 r 2 + s 2 s 3 . E) none of the above 4) 5) For s 3 t 3 + 2 r 2 - s 2 = 2, the partial derivative t r evaluated at r = 1, s = 1, t = 1 is A) 0. B) -2. C) 4 . D) - 4 3 . E) none of the above 5) 6) For x 2 + xy + yz + z 2 = 6, the partial derivative z y evaluated at x = 1, y = 2, z = 1 is A) - 3 2 B) - 5 2 C) -1 D) - 3 5 E) - 1 2 6) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

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Unformatted text preview: 7) Find y' if 3 x 2- 7 y 2 = 8. 7) 1 8) Find y' if xy = y 2 + 1. 8) 9) Find an equation of the tangent line to the curve x 2 + y + y 2 = 13 at the point (-1, 3). 9) 10) The demand equation for a product is p = 400 - 0.2 q 2 . Find the rate of change of quantity with respect to price. 10) 11) Suppose p = 500 - 0.01 q- 0.02 q is the demand equation for a product. Find the rate of change of quantity with respect to price. 11) 12) If 2 x 2 + 3 y 2 + 2 z 2 = 16, find ∂ z ∂ y . 12) 13) If x 2 y + xz + z 2 = 4, find ∂ z ∂ x . 13) 14) For 2 x 2 + 3 y 2 + 2 z 2 = 16, evaluate ∂ z ∂ y when x = 1, y = 2, z = -1. 14) 15) If z = 2 x 2 y + 3 xy + y 2 where x = r 2 + 2 rs and y = 2 r- 4 s , then by means of the chain rule, (a) find ∂ z ∂ s ; (b) evaluate when r = 1 and s = 0. 15) 2...
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Impl-dif-tut-que - 7 Find y if 3 x 2 7 y 2 = 8 7 1 8 Find y...

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