What is the sum of the infinite geometric series: 1 + 1/2 + 1/4 + 1/8 + ...?
1
2
4
8
Correct Answer :
B. 2
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Trapezoidal Rule
Simpson's Rule
Fundamental Theorem of Calculus
L'H�pital's Rule
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x = t, y = 0
x = 0, y = t
x = t, y = t
x = 0, y = 0
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n(a + d)
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n(a + d)/2
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0
1
p
undefined
What is the sum of the first n terms of an arithmetic series with first term a and common difference d?
n(a + d)
n(2a + (n-1)d)/2
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In polar coordinates, what is the equation of a circle with radius r and center at the origin?
r = 1
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r = 2?
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Cardioid
Spiral
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3^n
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2^n
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The chain rule states that if y = f(g(x)), then dy/dx is equal to:
f'(x) * g(x)
f'(g(x)) * g'(x)
f(x) * g(x)
f(x) * g'(x)
In polar coordinates, what is the equation of a circle with radius r and center at the origin?
r = 1
r = vx^2 + y^2
r = 2?
r = 2
What is the derivative of the function g(x) = e^(3x^2)?
6x * e^(3x^2)
3x^2 * e^(3x^2)
6x * e^(3x)
e^(3x)
What is the integral of 2x dx?
x^2 + C
x^2
x + C
2x^2 + C
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?
F(b) = F(a)
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F(b) - F(a) = ?(a to b) f(x) dx
F(b) - F(a) = 0
What is the order of the differential equation dy/dx = 3x^2 - 2y?
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Second order
Third order
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What is the derivative of the vector-valued function r(t) = ?
<2t, 3, 6t^2>
<2t, 3t, 6t^2>
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One arbitrary constant
No arbitrary constants
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What is the radius of convergence for the power series ?(n=0 to 8) (2^n*x^n/n!)?
1
2
8
0
What is the radius of convergence for the power series ?(n=0 to 8) (2^n*x^n/n!)?
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8
0
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1/x
x
e^x
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The concavity of f(x)
The slope of the tangent line to f(x)
The area under the curve of f(x)
If a curve C is parameterized by r(t) = , what type of curve is it?
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A circle
A parabola
An ellipse
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f(c) = 0
f'(c) = 0
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What is the general solution to the differential equation dy/dx + 2y = 4x?
y(x) = 2x^2 + C
y(x) = 2x^2 + 4x + C
y(x) = 2x^2 + 4x
y(x) = 2x^2
If f(x) = x^3 - 12x^2 + 45x, where does f(x) have a local maximum?
x = 3
x = 6
x = 9
x = 12
Which of the following parametric equations represents a horizontal line?
x = t, y = 0
x = 0, y = t
x = t, y = t
x = 0, y = 0
What is the limit of (e^x - 1)/x as x approaches 0?
0
1
e
undefined
The alternating series test can be used to determine the convergence of a series if the terms of the series:
Are all positive.
Alternate in sign and decrease in absolute value.
Are decreasing.
Are increasing.
What is the magnitude of the vector <3, 4, 5>?
v6
7
v50
25