Newton's Method with initial approximation x0 is used to approximate a real root of the equation x4 - 2 = 0. The value of Newton's Method iteration x1 is equal to

A) B) C) D) E) ± A) B) C) D) E) ±

A) < , n = 5 B) < , n = 4 C) < , n = 6 D) < , n = 4 E) none of the above A) < , n = 5 B) < , n = 4 C) < , n = 6 D) < , n = 4 E) none of the above

An open rectangular box with square base is to be made from 300 cm2 of material. What dimensions will result in a box with the largest possible volume?

A) 2 cm × 2 cm × 37 cm B) 10 cm × 10 cm × 5 cm C) 6 cm × 6 cm × 11 cm D) 11 cm × 11 cm × 7 cm E) 1 cm × 1 cm × 75 cm A) 2 cm × 2 cm × 37 cm B) 10 cm × 10 cm × 5 cm C) 6 cm × 6 cm × 11 cm D) 11 cm × 11 cm × 7 cm E) 1 cm × 1 cm × 75 cm

A) - B) -3 C) D) -ln 3 E) A) - B) -3 C) D) -ln 3 E)

Exam 5: More Applications of Differentiation

A lamp is shining on top of a vertical light post that is 540 centimetres tall. A girl is running away from the base of the light post at a constant rate so that her shadow is increasing at the rate of 15 cm/s and the tip of her shadow is moving away from the base at the rate of 90 cm/s. How tall is she?

(Essay)

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Question 101

Evaluate the limit x ln x.

(Multiple Choice)

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Question 102

Use information obtained from f and its first two derivatives to sketch the graph of the function f(x) = x³ - 2x² - 4x + 3.

(Essay)

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Question 103

Newton's Method with initial approximation x₀ is used to approximate a real root of the equation x⁴ - 2 = 0. The value of Newton's Method iteration x₁ is equal to

(Multiple Choice)

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Question 104

Find the extreme values of f(x) = x - 2 sin x on [0, $\pi$ ].

(Multiple Choice)

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Question 105

Find the solution of the equation + 5x = 0 to four decimal places using Newton's Method.

(Multiple Choice)

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Question 106

The equation xy + + = 6 defines y as a function of x near the point (1, 1). Find an approximate value for y at x = 1.1.

(Multiple Choice)

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Question 107

Given that < 2, find an estimate for the size of the error if the Maclaurin polynomial of degree n for is used to approximate = . How large need n be to ensure that this error is less than 10^-4?

(Multiple Choice)

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Question 108

What are the asymptotes of the graph of y = ?

(Multiple Choice)

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Question 109

An open rectangular box with square base is to be made from 300 cm² of material. What dimensions will result in a box with the largest possible volume?

(Multiple Choice)

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Question 110

The equation y = sin(x + y) - defines y as a function of x near the point . Find the linearization of that function at x = 0.

(Multiple Choice)

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Question 111

Use linear approximation to approximate .

(Multiple Choice)

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Question 112

Evaluate the limit . -

(Multiple Choice)

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Question 113

By considering the locations of its critical points, determine how many real zeros the function must have. Find them, correct to six decimal places.

(Multiple Choice)

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Question 114

Find the Taylor polynomial of degree 4 for the natural logarithm function ln x about x = 2.

(Multiple Choice)

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Question 115

Find a linear approximation suitable for estimating the number 244^2/5.

(Multiple Choice)

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Question 116

Find the largest possible volume of a right circular cylinder that is inscribed in a sphere of radius r.

(Multiple Choice)

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Question 117

Evaluate the limit .

(Multiple Choice)

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Question 118

A boat is pulled toward a dock by a rope with one end attached to the bow of the boat and the other end passing through a ring attached to the dock 2 metres higher than the bow of the boat. If the rope is pulled in at the rate of 0.5 metres per second, how fast is the boat approaching the dock when 3 metres of rope are out? (round to the nearest hundredth metre)

(Multiple Choice)

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Question 119

Let g be a polynomial function such that (x) = (x + 2)( - 10x -24). Find the x-coordinate of all inflection points of the graph of g.

(Multiple Choice)

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Question 120

Showing 101 - 120 of 130

Evaluate the limit x ln x.

Use information obtained from f and its first two derivatives to sketch the graph of the function f(x) = x³ - 2x² - 4x + 3.

Newton's Method with initial approximation x₀ is used to approximate a real root of the equation x⁴ - 2 = 0. The value of Newton's Method iteration x₁ is equal to

Find the extreme values of f(x) = x - 2 sin x on [0, $\pi$ ].

Find the solution of the equation + 5x = 0 to four decimal places using Newton's Method.

The equation xy + + = 6 defines y as a function of x near the point (1, 1). Find an approximate value for y at x = 1.1.

Given that < 2, find an estimate for the size of the error if the Maclaurin polynomial of degree n for is used to approximate = . How large need n be to ensure that this error is less than 10^-4?

What are the asymptotes of the graph of y = ?

An open rectangular box with square base is to be made from 300 cm² of material. What dimensions will result in a box with the largest possible volume?

The equation y = sin(x + y) - defines y as a function of x near the point . Find the linearization of that function at x = 0.

Use linear approximation to approximate .

Evaluate the limit . -

By considering the locations of its critical points, determine how many real zeros the function must have. Find them, correct to six decimal places.

Find the Taylor polynomial of degree 4 for the natural logarithm function ln x about x = 2.

Find a linear approximation suitable for estimating the number 244^2/5.

Find the largest possible volume of a right circular cylinder that is inscribed in a sphere of radius r.

Evaluate the limit .

Let g be a polynomial function such that (x) = (x + 2)( - 10x -24). Find the x-coordinate of all inflection points of the graph of g.

Preliminaries

Limits and Continuity

Differentiation

Transcendental Functions

Integration

Techniques of Integration

Applications of Integration

Conics, Parametric Curves, and Polar Curves

Sequences, Series, and Power Series

Vectors and Coordinate Geometry in 3-Space

Vector Functions and Curves

Partial Differentiation

Applications of Partial Derivatives

Multiple Integration

Vector Fields

Vector Calculus

Differential Forms and Exterior Calculus

Ordinary Differential Equations

Filters

Exam 5: More Applications of Differentiation

Evaluate the limit x ln x.

Use information obtained from f and its first two derivatives to sketch the graph of the function f(x) = x3 - 2x2 - 4x + 3.

Newton's Method with initial approximation x0 is used to approximate a real root of the equation x4 - 2 = 0. The value of Newton's Method iteration x1 is equal to

Find the extreme values of f(x) = x - 2 sin x on [0, π\piπ ].

Find the solution of the equation + 5x = 0 to four decimal places using Newton's Method.

The equation xy + + = 6 defines y as a function of x near the point (1, 1). Find an approximate value for y at x = 1.1.

Given that < 2, find an estimate for the size of the error if the Maclaurin polynomial of degree n for is used to approximate = . How large need n be to ensure that this error is less than 10-4?

What are the asymptotes of the graph of y = ?

An open rectangular box with square base is to be made from 300 cm2 of material. What dimensions will result in a box with the largest possible volume?

The equation y = sin(x + y) - defines y as a function of x near the point . Find the linearization of that function at x = 0.

Use linear approximation to approximate .

Evaluate the limit . -

By considering the locations of its critical points, determine how many real zeros the function must have. Find them, correct to six decimal places.

Find the Taylor polynomial of degree 4 for the natural logarithm function ln x about x = 2.

Find a linear approximation suitable for estimating the number 2442/5.

Find the largest possible volume of a right circular cylinder that is inscribed in a sphere of radius r.

Evaluate the limit .

Let g be a polynomial function such that (x) = (x + 2)( - 10x -24). Find the x-coordinate of all inflection points of the graph of g.

Preliminaries

Limits and Continuity

Differentiation

Transcendental Functions

Integration

Techniques of Integration

Applications of Integration

Conics, Parametric Curves, and Polar Curves

Sequences, Series, and Power Series

Vectors and Coordinate Geometry in 3-Space

Vector Functions and Curves

Partial Differentiation

Applications of Partial Derivatives

Multiple Integration

Vector Fields

Vector Calculus

Differential Forms and Exterior Calculus

Ordinary Differential Equations

Filters

Use information obtained from f and its first two derivatives to sketch the graph of the function f(x) = x³ - 2x² - 4x + 3.

Newton's Method with initial approximation x₀ is used to approximate a real root of the equation x⁴ - 2 = 0. The value of Newton's Method iteration x₁ is equal to

Find the extreme values of f(x) = x - 2 sin x on [0, $\pi$ ].

Given that < 2, find an estimate for the size of the error if the Maclaurin polynomial of degree n for is used to approximate = . How large need n be to ensure that this error is less than 10^-4?

An open rectangular box with square base is to be made from 300 cm² of material. What dimensions will result in a box with the largest possible volume?

Find a linear approximation suitable for estimating the number 244^2/5.