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1. 2. Determine the tangent line to the graph of 3(x+y)-100xy at the point (3,1) Find given sin(x)=2x+5

1. 2. Determine the tangent line to the graph of 3(x+y)-100xy at the point (3,1) Find given sin(x)=2x+5

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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1. 2. 3. 4. 5. 6. 7. Determine the tangent line to the graph of 3(x+y)-100xy at the point (3,1). Find given sin(x)=2x+5. Find the slope of the tangent t lin to the ellipse x + 4y - 4at the point (1) At what rate (in cubic inches per second) is soda being sucked out of a cylindrical glass that is 6 inches tall and has a radius of 2 inches given that the depth of the soda is decreasing at a constant rate of 0.25 inches per second? A particle moves along the curve y=√1+x. As it reaches the point (2,3), the y- coordinate is increasing at a rate of 4 cm/s. How fast is the x-coordinate of the point changing at the instant? A spotlight on the ground shines on a vertical wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 1.6 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building? A water-skier skis over the ramp shown in the figure at a speed of 30 ft/sec. How fast is she rising as she leaves the ramp? 15 ft 4 ft
Transcribed Image Text:1. 2. 3. 4. 5. 6. 7. Determine the tangent line to the graph of 3(x+y)-100xy at the point (3,1). Find given sin(x)=2x+5. Find the slope of the tangent t lin to the ellipse x + 4y - 4at the point (1) At what rate (in cubic inches per second) is soda being sucked out of a cylindrical glass that is 6 inches tall and has a radius of 2 inches given that the depth of the soda is decreasing at a constant rate of 0.25 inches per second? A particle moves along the curve y=√1+x. As it reaches the point (2,3), the y- coordinate is increasing at a rate of 4 cm/s. How fast is the x-coordinate of the point changing at the instant? A spotlight on the ground shines on a vertical wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 1.6 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building? A water-skier skis over the ramp shown in the figure at a speed of 30 ft/sec. How fast is she rising as she leaves the ramp? 15 ft 4 ft
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