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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

Correct Answer :

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


Related Questions

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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 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

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

What is the order of the differential equation dy/dx = 3x^2 - 2y?

A. First order

B. Second order

C. Third order

D. Fourth order

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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 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

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 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 derivative of ln(x) with respect to x?

A. 1/x

B. x

C. e^x

D. 0

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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

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 is the nth term of the geometric sequence: 3, 6, 12, 24, ...?

A. 3^n

B. 3^(n+1)

C. 2^n

D. 2^(n+1)

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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

If F(x) is an antiderivative of f(x), what is the relationship between F(b) and F(a) in the context of the Fundamental Theorem of Calculus?

A. F(b) = F(a)

B. F(b) - F(a) = f(b) - f(a)

C. F(b) - F(a) = ?(a to b) f(x) dx

D. F(b) - F(a) = 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 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

The work done by a force F(x) in moving an object along a straight line from x = a to x = b is given by the integral ?(a to b) F(x) dx. What does this integral represent?

A. The average value of F(x) on the interval [a, b]

B. The derivative of F(x) with respect to x

C. The area under the curve of F(x) from a to b

D. The total work done by the force

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4

The alternating series test can be used to determine the convergence of a series if the terms of the series:

A. Are all positive.

B. Alternate in sign and decrease in absolute value.

C. Are decreasing.

D. Are increasing.

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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.

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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

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

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

What is the correct answer?

4

What is the derivative of the function g(x) = e^(3x^2)?

A. 6x * e^(3x^2)

B. 3x^2 * e^(3x^2)

C. 6x * e^(3x)

D. e^(3x)

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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

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 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

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

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

A. 1

B. 0

C. 2

D. undefined