7. Find the differential dy of y = vx. Then use the differential to approximate vI101. 8. Consider the function f(x) = v9 – x. Use the limit definition of a derivative to compute f'(x). Find the domain of f and f'. Find the tangent line to the curve f at x = 5. Note: f'(x) = lim f(x+h)-f(x) 9. Find (f-1)'(7) without finding the inverse function where f (x) = 5 – 2x. 10. Use the Second Derivative Test to find all relative extrema of the function f(x) = 5x² – 3x³. 11. Consider the function f(x) = x + cot () on the interval (). Find all the critical points inside the interval and then determine the absolute maximum and absolute minimum value of f on (;. ). 12. A paper cup has the shape of a cone with height 10 cm and radius 3 cm at the top. If water is poured into the cup at a rate of 2 cm² /s, how fast is the water level rising when the water is 5 cm deep? 13. Use Newton's method to find the three roots of the following equation: x³ – 5x – 3 = 0. 14. The amount of air present in the lungs is modeled using the function f (t) =sin () where t is in second. A full breathing cycle is estimated to take about five seconds. Find the average amount of air in the lungs in one full breathing cycle. 15. Apply Rolle's Theorem to f (x) = sin x on the interval [0,27]. Find all values of c e (0,27) such that f'(c) = 0. Why does Rolle's Theorem apply here? 16. Apply the Mean Value Theorem to f(x) = 5 – on the interval [1,4]. Find all values of CE (1,4) such that f' (c) = -7, wWhy does the Mean Value Theorem apply here? 4-1
7. Find the differential dy of y = vx. Then use the differential to approximate vI101. 8. Consider the function f(x) = v9 – x. Use the limit definition of a derivative to compute f'(x). Find the domain of f and f'. Find the tangent line to the curve f at x = 5. Note: f'(x) = lim f(x+h)-f(x) 9. Find (f-1)'(7) without finding the inverse function where f (x) = 5 – 2x. 10. Use the Second Derivative Test to find all relative extrema of the function f(x) = 5x² – 3x³. 11. Consider the function f(x) = x + cot () on the interval (). Find all the critical points inside the interval and then determine the absolute maximum and absolute minimum value of f on (;. ). 12. A paper cup has the shape of a cone with height 10 cm and radius 3 cm at the top. If water is poured into the cup at a rate of 2 cm² /s, how fast is the water level rising when the water is 5 cm deep? 13. Use Newton's method to find the three roots of the following equation: x³ – 5x – 3 = 0. 14. The amount of air present in the lungs is modeled using the function f (t) =sin () where t is in second. A full breathing cycle is estimated to take about five seconds. Find the average amount of air in the lungs in one full breathing cycle. 15. Apply Rolle's Theorem to f (x) = sin x on the interval [0,27]. Find all values of c e (0,27) such that f'(c) = 0. Why does Rolle's Theorem apply here? 16. Apply the Mean Value Theorem to f(x) = 5 – on the interval [1,4]. Find all values of CE (1,4) such that f' (c) = -7, wWhy does the Mean Value Theorem apply here? 4-1
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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![7. Find the differential dy of y = Vx. Then use the differential to approximate v101.
8. Consider the function f(x) = v9 – x. Use the limit definition of a derivative to compute
f'(x). Find the domain of f and f'. Find the tangent line to the curve f at x = 5.
f(x+h)-f(x)
Note: f'(x) = lim
9. Find (f-1)'(7) without finding the inverse function where f(x) = 5 – 2x?.
10. Use the Second Derivative Test to find all relative extrema of the function
f(x) = 5x – 3x*.
11. Consider the function f(x) = x + cot () on the interval F.). Find all the critical
points inside the interval and then determine the absolute maximum and absolute
minimum value of f on
12. A paper cup has the shape of a cone with height 10 cm and radius 3 cm at the top. If
water is poured into the cup at a rate of 2 cm? /s, how fast is the water level rising when
the water is 5 cm deep?
13. Use Newton's method to find the three roots of the following equation: x? – 5x – 3 = 0.
14. The amount of air present in the lungs is modeled using the function f (t) = sin ()
where t is in second. A full breathing cycle is estimated to take about five seconds. Find
the average amount of air in the lungs in one full breathing cycle.
15. Apply Rolle's Theorem to f(x) = sin x on the interval [0,27]. Find all values of c e
(0,27) such that f'(c) = 0. Why does Rolle's Theorem apply here?
16. Apply the Mean Value Theorem to f(x) = 5 -on the interval [1,4]. Find all values of
Ce (1,4) such that f'(c) = -1 Why does the Mean Value Theorem apply here?
17. A metal storage tank with volume V constructed in shape of a right cylinder
surmounted by a hemisphere. What dimension will require the least amount of metal?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb40fa447-d3c2-41e2-8596-d1d31b5ac1d4%2F8d4ece46-373b-41bc-a23d-e4b0b73aa60e%2Flg9227r_processed.png&w=3840&q=75)
Transcribed Image Text:7. Find the differential dy of y = Vx. Then use the differential to approximate v101.
8. Consider the function f(x) = v9 – x. Use the limit definition of a derivative to compute
f'(x). Find the domain of f and f'. Find the tangent line to the curve f at x = 5.
f(x+h)-f(x)
Note: f'(x) = lim
9. Find (f-1)'(7) without finding the inverse function where f(x) = 5 – 2x?.
10. Use the Second Derivative Test to find all relative extrema of the function
f(x) = 5x – 3x*.
11. Consider the function f(x) = x + cot () on the interval F.). Find all the critical
points inside the interval and then determine the absolute maximum and absolute
minimum value of f on
12. A paper cup has the shape of a cone with height 10 cm and radius 3 cm at the top. If
water is poured into the cup at a rate of 2 cm? /s, how fast is the water level rising when
the water is 5 cm deep?
13. Use Newton's method to find the three roots of the following equation: x? – 5x – 3 = 0.
14. The amount of air present in the lungs is modeled using the function f (t) = sin ()
where t is in second. A full breathing cycle is estimated to take about five seconds. Find
the average amount of air in the lungs in one full breathing cycle.
15. Apply Rolle's Theorem to f(x) = sin x on the interval [0,27]. Find all values of c e
(0,27) such that f'(c) = 0. Why does Rolle's Theorem apply here?
16. Apply the Mean Value Theorem to f(x) = 5 -on the interval [1,4]. Find all values of
Ce (1,4) such that f'(c) = -1 Why does the Mean Value Theorem apply here?
17. A metal storage tank with volume V constructed in shape of a right cylinder
surmounted by a hemisphere. What dimension will require the least amount of metal?
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