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4

The Alternating Series Test can be used to determine the convergence of a series if:

A. The series terms are all positive.

B. The series terms alternate in sign and decrease in absolute value.

C. The series has a finite number of terms.

D. The series has a constant rate of growth.

Correct Answer :

B. The series terms alternate in sign and decrease in absolute value.


Related Questions

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4

What is the limit of (sin(x))/x as x approaches 0?

A. 0

B. 1

C. p

D. undefined

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4

In polar coordinates, what is the equation of a circle with radius r and center at the origin?

A. r = 1

B. r = vx^2 + y^2

C. r = 2?

D. r = 2

What is the correct answer?

4

What is the limit of (e^x - 1)/x as x approaches 0?

A. 0

B. 1

C. e

D. undefined

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4

What is the integral of 2x dx?

A. x^2 + C

B. x^2

C. x + C

D. 2x^2 + C

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4

What is the radius of convergence for the power series ?(n=0 to 8) (2^n*x^n/n!)?

A. 1

B. 2

C. 8

D. 0

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4

If a curve C is parameterized by r(t) = , what type of curve is it?

A. A line

B. A circle

C. A parabola

D. An ellipse

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4

If a function f(x) has a local minimum at x = a, what can be said about f'(a) and f''(a)?

A. f'(a) = 0 and f''(a) < 0

B. f'(a) < 0 and f''(a) = 0

C. f'(a) = 0 and f''(a) = 0

D. f'(a) > 0 and f''(a) > 0

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4

Which of the following parametric equations represents a horizontal line?

A. x = t, y = 0

B. x = 0, y = t

C. x = t, y = t

D. x = 0, y = 0

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4

What is the radius of convergence for the power series ?(n=0 to 8) (2^n*x^n/n!)?

A. 1

B. 2

C. 8

D. 0

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4

What does the second derivative f''(x) tell you about a function f(x)?

A. The rate of change of f(x)

B. The concavity of f(x)

C. The slope of the tangent line to f(x)

D. The area under the curve of f(x)

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4

Separation of variables is a technique commonly used to solve which type of differential equation?

A. Linear differential equations

B. Exact differential equations

C. First-order ordinary differential equations

D. Second-order ordinary differential equations

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4

What is the sum of the first n terms of an arithmetic series with first term a and common difference d?

A. n(a + d)

B. n(2a + (n-1)d)/2

C. n(a + d)/2

D. a + nd

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4

What is the general solution to the differential equation dy/dx + 2y = 4x?

A. y(x) = 2x^2 + C

B. y(x) = 2x^2 + 4x + C

C. y(x) = 2x^2 + 4x

D. y(x) = 2x^2

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4

What is the Maclaurin series expansion of sin(x)?

A. x - (x^3)/3! + (x^5)/5! - (x^7)/7! + ...

B. x + (x^3)/3! + (x^5)/5! + (x^7)/7! + ...

C. 1 - x + (x^2)/2 - (x^3)/3 + ...

D. e^x

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4

If a curve C is parameterized by r(t) = , what type of curve is it?

A. A line

B. A circle

C. A parabola

D. An ellipse

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4

Which statement is true about the continuity of a function at a point?

A. The function must be differentiable at that point.

B. The function must have a removable discontinuity at that point.

C. The function must have a jump discontinuity at that point.

D. The function must have the same limit from the left and right at that point.

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4

The polar equation r = 2 + 3cos(?) represents a:

A. Circle

B. Parabola

C. Cardioid

D. Spiral

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4

What is the magnitude of the vector <3, 4, 5>?

A. v6

B. 7

C. v50

D. 25

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4

What is the curl of the vector field F(x, y, z) = <2xy, x^2 - y^2, 3z^2>?

A. <0, 0, 0>

B. <0, 2z, 0>

C. <2, -2, 0>

D. <0, 0, 6z>

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4

The Mean Value Theorem for Integrals states that for a continuous function f(x) on the interval [a, b], there exists a c in (a, b) such that:

A. f(c) = 0

B. f'(c) = 0

C. f(c) = (b - a) * f'(c)

D. f'(c) = 1/(b - a)

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4

The chain rule states that if y = f(g(x)), then dy/dx is equal to:

A. f'(x) * g(x)

B. f'(g(x)) * g'(x)

C. f(x) * g(x)

D. f(x) * g'(x)

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4

If f(x) = x^3 - 12x^2 + 45x, where does f(x) have a local maximum?

A. x = 3

B. x = 6

C. x = 9

D. x = 12

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4

What is the curl of the vector field F(x, y, z) = <2xy, x^2 - y^2, 3z^2>?

A. <0, 0, 0>

B. <0, 2z, 0>

C. <2, -2, 0>

D. <0, 0, 6z>

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4

Which test can be used to determine the convergence or divergence of a series when the terms are positive, decreasing, and approach zero?

A. Integral Test

B. Ratio Test

C. Alternating Series Test

D. Divergence Test

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4

What is the sum of the first n terms of an arithmetic series with first term a and common difference d?

A. n(a + d)

B. n(2a + (n-1)d)/2

C. n(a + d)/2

D. a + nd

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4

Which of the following is a method for approximating definite integrals using rectangles?

A. Trapezoidal Rule

B. Simpson's Rule

C. Fundamental Theorem of Calculus

D. L'H�pital's Rule

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4

In polar coordinates, what is the equation of a circle with radius r and center at the origin?

A. r = 1

B. r = vx^2 + y^2

C. r = 2?

D. r = 2

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4

What is the derivative of ln(x) with respect to x?

A. 1/x

B. x

C. e^x

D. 0

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4

What is the derivative of the vector-valued function r(t) = ?

A. <2t, 3, 6t^2>

B. <2t, 3t, 6t^2>

C.

D. <2t, 3t, 4t^2>

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4

What is the limit of (x^2 - 1)/(x - 1) as x approaches 1?

A. 1

B. 0

C. 2

D. undefined