- Answer All Questions By Showing The Working Completely 1 (109.11 KiB) Viewed 35 times
Answer all questions by showing the working completely.
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answerhappygod
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Answer all questions by showing the working completely.
Answer all questions by showing the working completely.
Work Problem (60 points) You must provide a clear and detailed solution step by step for each question. Question 1 [20 pts] Let C be a curve defined by the vector equation r(t)= <8t³ – 5t, 8t³ +9t, e8t³-5t>. - a) [08 pts] Show that the point P(3, 17, e³) lies on the curve C. b) [12 pts] Find parametric equations for the tangent line to the curve C at the point P. Question 2 [20 pts] Given the function of two variables ƒ(x, y) = −(x − 7)² In²(y + 5)−(5x + 7y)². - a) [12 pts] Find all the first partial derivatives of the function f(x, y). b) [08 pts] Determine the point(s) where the following function is defined g(x, y) = √(x − 7)² In²(y + 5)−25x² − 70xy − 49y². Question 3 [20 pts] Find the limit, if it exists, or show that the limit does not exist. a) [10 pts] b) [10 pts] lim (x,y) →(0,0) lim (x,y)→(0,0) 7x²+5y 5y 49x²-98xy+49y² 7x-7y
Work Problem (60 points) You must provide a clear and detailed solution step by step for each question. Question 1 [20 pts] Let C be a curve defined by the vector equation r(t)= <8t³ – 5t, 8t³ +9t, e8t³-5t>. - a) [08 pts] Show that the point P(3, 17, e³) lies on the curve C. b) [12 pts] Find parametric equations for the tangent line to the curve C at the point P. Question 2 [20 pts] Given the function of two variables ƒ(x, y) = −(x − 7)² In²(y + 5)−(5x + 7y)². - a) [12 pts] Find all the first partial derivatives of the function f(x, y). b) [08 pts] Determine the point(s) where the following function is defined g(x, y) = √(x − 7)² In²(y + 5)−25x² − 70xy − 49y². Question 3 [20 pts] Find the limit, if it exists, or show that the limit does not exist. a) [10 pts] b) [10 pts] lim (x,y) →(0,0) lim (x,y)→(0,0) 7x²+5y 5y 49x²-98xy+49y² 7x-7y