Some c ∈ [ a , b ] such that f ′ ( c ) = 0 if Rolle’s theorem holds for the function f ( x ) = tan x and the explanation if the Rolle’s theorem does not hold for the function f ( x ) = tan x .

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Answer 1

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Chapter 3.2, Problem 21E

To determine

To calculate: Some c∈[ a,b ] such that f′(c)=0 if Rolle’s theorem holds for the function f(x)=tanx and the explanation if the Rolle’s theorem does not hold for the function f(x)=tanx.

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f'(x)

A body of mass m at the top of a 100 m high tower is thrown vertically upward with an initial velocity of 10 m/s. Assume that the air resistance FD acting on the body is proportional to the velocity V, so that FD=kV. Taking g = 9.75 m/s2 and k/m = 5 s, determine: a) what height the body will reach at the top of the tower, b) how long it will take the body to touch the ground, and c) the velocity of the body when it touches the ground.

A chemical reaction involving the interaction of two substances A and B to form a new compound X is called a second order reaction. In such cases it is observed that the rate of reaction (or the rate at which the new compound is formed) is proportional to the product of the remaining amounts of the two original substances. If a molecule of A and a molecule of B combine to form a molecule of X (i.e., the reaction equation is A + B ⮕ X), then the differential equation describing this specific reaction can be expressed as: dx/dt = k(a-x)(b-x) where k is a positive constant, a and b are the initial concentrations of the reactants A and B, respectively, and x(t) is the concentration of the new compound at any time t. Assuming that no amount of compound X is present at the start, obtain a relationship for x(t). What happens when t ⮕∞?

Answer 2

Question

Chapter 3.2, Problem 21E

To determine

To calculate: Some c∈[ a,b ] such that f′(c)=0 if Rolle’s theorem holds for the function f(x)=tanx and the explanation if the Rolle’s theorem does not hold for the function f(x)=tanx.

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Answer 3

Question

Chapter 3.2, Problem 21E

To determine

To calculate: Some c∈[ a,b ] such that f′(c)=0 if Rolle’s theorem holds for the function f(x)=tanx and the explanation if the Rolle’s theorem does not hold for the function f(x)=tanx.

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Answer 4

Question

Chapter 3.2, Problem 21E

To determine

To calculate: Some c∈[ a,b ] such that f′(c)=0 if Rolle’s theorem holds for the function f(x)=tanx and the explanation if the Rolle’s theorem does not hold for the function f(x)=tanx.

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Answer 5

Chapter 3.2, Problem 21E

To determine

To calculate: Some c∈[ a,b ] such that f′(c)=0 if Rolle’s theorem holds for the function f(x)=tanx and the explanation if the Rolle’s theorem does not hold for the function f(x)=tanx.

Answer 6

Chapter 3.2, Problem 21E

To determine

To calculate: Some c∈[ a,b ] such that f′(c)=0 if Rolle’s theorem holds for the function f(x)=tanx and the explanation if the Rolle’s theorem does not hold for the function f(x)=tanx.

Answer 7

Chapter 3.2, Problem 21E

To determine

To calculate: Some c∈[ a,b ] such that f′(c)=0 if Rolle’s theorem holds for the function f(x)=tanx and the explanation if the Rolle’s theorem does not hold for the function f(x)=tanx.

Answer 8

Expert Solution & Answer

Answer 9

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Answer 10

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Some c ∈ [ a , b ] such that f ′ ( c ) = 0 if Rolle’s theorem holds for the function f ( x ) = tan x and the explanation if the Rolle’s theorem does not hold for the function f ( x ) = tan x .

Solution Summary: The author explains that the Rolle's theorem is inapplicable for the function f(x)=mathrmtanx because it is not continuous on

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To calculate: Some c∈[ a,b ] such that f′(c)=0 if Rolle’s theorem holds for the function f(x)=tanx and the explanation if the Rolle’s theorem does not hold for the function f(x)=tanx.

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