A) B) 1 C) D) - E) - A) B) 1 C) D) - E) -

A) 1 B) C) 0 D) $\infty$ E) A) 1 B) C) 0 D) $\infty$ E)

A) -2 B) -1 C) 0 D) $\infty$ E) 1 A) -2 B) -1 C) 0 D) $\infty$ E) 1

Exam 5: More Applications of Differentiation

Given f(x) = , c = -1, n = 2. (i) Write out Taylor's Formula with Lagrange Remainder for the function f and the specified values of c and n. (ii) Use part (i) to estimate the value of and estimate the error involved in the approximation.

(Essay)

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Question 81

Find all local extreme values of the function f(x) = 2 + 3 - 12x + 13 and their locations.

(Multiple Choice)

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Question 82

Evaluate the limit .

(Multiple Choice)

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Question 83

Evaluate the limit .

(Multiple Choice)

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Question 84

Find any extreme values and points of inflection of the function f(x) = x⁴ - 4 + 10.

(Multiple Choice)

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Question 85

Determine the concavity and inflections of f(x) = .

(Multiple Choice)

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Question 86

Let g(x) = 3(x - 1)^2/3 - x. Which of the following statements is true?

(Multiple Choice)

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Question 87

The function f(x) = 4 + k - has a maximum value at x = 2. Find k.

(Multiple Choice)

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Question 88

Evaluate the limit .

(Multiple Choice)

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Question 89

Determine the concavity of f(x) = cos x + sin x on [0, 2 $\pi$ ] and identify any points of inflection.

(Multiple Choice)

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Question 90

Which of the following statements best describes the graph of the function f(x) = ?

(Multiple Choice)

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Question 91

A cylindrical can constructed from sheet metal holds a litre of oil. Find the radius of the can that will minimize the area of metal used to make the can. (Use 1 L = 1000 cm³.)

(Multiple Choice)

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Question 92

Find the area of the largest rectangle that can be inscribed in the ellipse + = 1.

(Multiple Choice)

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Question 93

Find the maximum value of the function f(x) = .

(Multiple Choice)

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Question 94

A lamp is 3 metres high on a post located 5 metres from a vertical wall. A 2 metre tall man walks toward the wall from the lamppost on a path perpendicular to the wall. He is walking at a rate of 1 metre per second. When he is 1 metre from the wall, how fast is the shadow of his head moving up the wall?

(Multiple Choice)

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Question 95

Find two nonnegative numbers whose sum is 9 such that the sum of one number and the square of the other number is a maximum.

(Multiple Choice)

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Question 96

Find the absolute maximum and absolute minimum values of the function f(x) = $Find the absolute maximum and absolute minimum values of the function f(x) = - , -4 \le x \le -1.$ - $Find the absolute maximum and absolute minimum values of the function f(x) = - , -4 \le x \le -1.$ , -4 $\le$ x $\le$ -1.

(Multiple Choice)

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Question 97

Use Newton's Method to find the x coordinate of a point on the curve y = x³ + 1 such that the tangent line to the curve at that point passes through the point (2, 0). Give your answer accurate to three decimal places.

(Multiple Choice)

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Question 98

A water trough is 10 m long and has vertical cross-sections perpendicular to its long axis with the shape of an isosceles trapezoid that is 30 cm wide at the bottom, 80 cm wide at the top, and has height of 50 cm. If the trough is being filled with water at the rate of 0.2 cubic metres per minute, how fast is the water level rising when the water is 30 cm deep?

(Multiple Choice)

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Question 99

Let f(x) = (x). Find the Taylor polynomial of f of degree 2 about c = 1.

(Multiple Choice)

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Question 100

Showing 81 - 100 of 130

Given f(x) = , c = -1, n = 2. (i) Write out Taylor's Formula with Lagrange Remainder for the function f and the specified values of c and n. (ii) Use part (i) to estimate the value of and estimate the error involved in the approximation.

Find all local extreme values of the function f(x) = 2 + 3 - 12x + 13 and their locations.

Evaluate the limit .

Evaluate the limit .

Find any extreme values and points of inflection of the function f(x) = x⁴ - 4 + 10.

Determine the concavity and inflections of f(x) = .

Let g(x) = 3(x - 1)^2/3 - x. Which of the following statements is true?

The function f(x) = 4 + k - has a maximum value at x = 2. Find k.

Evaluate the limit .

Determine the concavity of f(x) = cos x + sin x on [0, 2 $\pi$ ] and identify any points of inflection.

Which of the following statements best describes the graph of the function f(x) = ?

A cylindrical can constructed from sheet metal holds a litre of oil. Find the radius of the can that will minimize the area of metal used to make the can. (Use 1 L = 1000 cm³.)

Find the area of the largest rectangle that can be inscribed in the ellipse + = 1.

Find the maximum value of the function f(x) = .

Find two nonnegative numbers whose sum is 9 such that the sum of one number and the square of the other number is a maximum.

Use Newton's Method to find the x coordinate of a point on the curve y = x³ + 1 such that the tangent line to the curve at that point passes through the point (2, 0). Give your answer accurate to three decimal places.

Let f(x) = (x). Find the Taylor polynomial of f of degree 2 about c = 1.

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

Given f(x) = , c = -1, n = 2. (i) Write out Taylor's Formula with Lagrange Remainder for the function f and the specified values of c and n. (ii) Use part (i) to estimate the value of and estimate the error involved in the approximation.

Find all local extreme values of the function f(x) = 2 + 3 - 12x + 13 and their locations.

Evaluate the limit .

Evaluate the limit .

Find any extreme values and points of inflection of the function f(x) = x4 - 4 + 10.

Determine the concavity and inflections of f(x) = .

Let g(x) = 3(x - 1)2/3 - x. Which of the following statements is true?

The function f(x) = 4 + k - has a maximum value at x = 2. Find k.

Evaluate the limit .

Determine the concavity of f(x) = cos x + sin x on [0, 2 π\piπ ] and identify any points of inflection.

Which of the following statements best describes the graph of the function f(x) = ?

A cylindrical can constructed from sheet metal holds a litre of oil. Find the radius of the can that will minimize the area of metal used to make the can. (Use 1 L = 1000 cm3.)

Find the area of the largest rectangle that can be inscribed in the ellipse + = 1.

Find the maximum value of the function f(x) = .

Find two nonnegative numbers whose sum is 9 such that the sum of one number and the square of the other number is a maximum.

Find the absolute maximum and absolute minimum values of the function f(x) = - , -4 ≤\le≤ x ≤\le≤ -1.

Use Newton's Method to find the x coordinate of a point on the curve y = x3 + 1 such that the tangent line to the curve at that point passes through the point (2, 0). Give your answer accurate to three decimal places.

Let f(x) = (x). Find the Taylor polynomial of f of degree 2 about c = 1.

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

Find any extreme values and points of inflection of the function f(x) = x⁴ - 4 + 10.

Let g(x) = 3(x - 1)^2/3 - x. Which of the following statements is true?

Determine the concavity of f(x) = cos x + sin x on [0, 2 $\pi$ ] and identify any points of inflection.

A cylindrical can constructed from sheet metal holds a litre of oil. Find the radius of the can that will minimize the area of metal used to make the can. (Use 1 L = 1000 cm³.)

Use Newton's Method to find the x coordinate of a point on the curve y = x³ + 1 such that the tangent line to the curve at that point passes through the point (2, 0). Give your answer accurate to three decimal places.