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1. Use implicit differentiation to find if y? = x*siny. 2. Find the value of given the equation 6x³ + 3x³y + 3y? = 9 at the point (1,1). 3. Let 5x3 – 2x?y + 2y² = 9. Find if = 3,x = 1, and y = 1. dt dt 4. Let A =bh. Find A if = -2, b = 3, = -1,h = 5. dt dt 5. Suppose that a 15 foot ladder is leaning against a building and that the base of the ladde sliding away from the building at a rate of 3 feet per second. How fast is the top of the l sliding down the building when the ladder is 10 feet from the base of the building?

1. Use implicit differentiation to find if y? = x*siny. 2. Find the value of given the equation 6x³ + 3x³y + 3y? = 9 at the point (1,1). 3. Let 5x3 – 2x?y + 2y² = 9. Find if = 3,x = 1, and y = 1. dt dt 4. Let A =bh. Find A if = -2, b = 3, = -1,h = 5. dt dt 5. Suppose that a 15 foot ladder is leaning against a building and that the base of the ladde sliding away from the building at a rate of 3 feet per second. How fast is the top of the l sliding down the building when the ladder is 10 feet from the base of the building?

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. Use implicit differentiation to find if y? = x*siny. 2. Find the value of given the equation 6x³ + 3x³y + 3y? = 9 at the point (1,1). 3. Let 5x3 – 2x?y + 2y² = 9. Find if = 3,x = 1, and y = 1. dt dt 4. Let A = bh. Find A if d = -2, b = 3, = -1, h = 5. dt 5. Suppose that a 15 foot ladder is leaning against a building and that the base of the ladder is sliding away from the building at a rate of 3 feet per second. How fast is the top of the ladder sliding down the building when the ladder is 10 feet from the base of the building? 6. Suppose that a red spherical balloon is being deflated and the radius is decreasing at a rate of 3 inches per seconds. How fast is the volume changing when the radius of the balloon is 12 inches? Note: V = ar3
Transcribed Image Text:1. Use implicit differentiation to find if y? = x*siny. 2. Find the value of given the equation 6x³ + 3x³y + 3y? = 9 at the point (1,1). 3. Let 5x3 – 2x?y + 2y² = 9. Find if = 3,x = 1, and y = 1. dt dt 4. Let A = bh. Find A if d = -2, b = 3, = -1, h = 5. dt 5. Suppose that a 15 foot ladder is leaning against a building and that the base of the ladder is sliding away from the building at a rate of 3 feet per second. How fast is the top of the ladder sliding down the building when the ladder is 10 feet from the base of the building? 6. Suppose that a red spherical balloon is being deflated and the radius is decreasing at a rate of 3 inches per seconds. How fast is the volume changing when the radius of the balloon is 12 inches? Note: V = ar3
7. Suppose a 15 foot ladder is leaning against a building. Let x be the distance in feet that the ladder is from the base of the building, and y is the distance of the top of the ladder from the base of shipbuilding, see Figure 1. Suppse the base of the ladder is sliding away from the dx building at a rate of 3 feet per second when it is nine feet from the base, so that x = 9 and 3. dy to be positive or negative. Explain dt a) Do you expect b) Now compute dy to find how fast the top of the ladder is moving. c) Explain what happens when the ladder is 20 feet from the building (i.e. if r = 20). 15 Feet
Transcribed Image Text:7. Suppose a 15 foot ladder is leaning against a building. Let x be the distance in feet that the ladder is from the base of the building, and y is the distance of the top of the ladder from the base of shipbuilding, see Figure 1. Suppse the base of the ladder is sliding away from the dx building at a rate of 3 feet per second when it is nine feet from the base, so that x = 9 and 3. dy to be positive or negative. Explain dt a) Do you expect b) Now compute dy to find how fast the top of the ladder is moving. c) Explain what happens when the ladder is 20 feet from the building (i.e. if r = 20). 15 Feet
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