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
Correct Answer :
D. r = 2
Related Questions
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
n(a + d)/2
a + nd
What is the curl of the vector field F(x, y, z) = <2xy, x^2 - y^2, 3z^2>?
<0, 0, 0>
<0, 2z, 0>
<2, -2, 0>
<0, 0, 6z>
Which of the following is a method for approximating definite integrals using rectangles?
Trapezoidal Rule
Simpson's Rule
Fundamental Theorem of Calculus
L'H�pital's Rule
If a function f(x) has a local minimum at x = a, what can be said about f'(a) and f''(a)?
f'(a) = 0 and f''(a) < 0
f'(a) < 0 and f''(a) = 0
f'(a) = 0 and f''(a) = 0
f'(a) > 0 and f''(a) > 0
What is the integral of 2x dx?
x^2 + C
x^2
x + C
2x^2 + C
Which test can be used to determine the convergence or divergence of a series when the terms are positive, decreasing, and approach zero?
Integral Test
Ratio Test
Alternating Series Test
Divergence Test
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?
The average value of F(x) on the interval [a, b]
The derivative of F(x) with respect to x
The area under the curve of F(x) from a to b
The total work done by the force
Separation of variables is a technique commonly used to solve which type of differential equation?
Linear differential equations
Exact differential equations
First-order ordinary differential equations
Second-order ordinary differential equations
A solution to a first-order linear homogeneous differential equation always has:
Two arbitrary constants
One arbitrary constant
No arbitrary constants
Three arbitrary constants
What is the order of the differential equation dy/dx = 3x^2 - 2y?
First order
Second order
Third order
Fourth order
What is the radius of convergence for the power series ?(n=0 to 8) (2^n*x^n/n!)?
1
2
8
0
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 derivative of the function g(x) = e^(3x^2)?
6x * e^(3x^2)
3x^2 * e^(3x^2)
6x * e^(3x)
e^(3x)
If a curve C is parameterized by r(t) = , what type of curve is it?
A line
A circle
A parabola
An ellipse
What is the sum of the infinite geometric series: 1 + 1/2 + 1/4 + 1/8 + ...?
1
2
4
8
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 limit of (x^2 - 1)/(x - 1) as x approaches 1?
1
0
2
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What is the magnitude of the vector <3, 4, 5>?
v6
7
v50
25
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
What is the derivative of the vector-valued function r(t) = ?
<2t, 3, 6t^2>
<2t, 3t, 6t^2>
<2t, 3t, 4t^2>
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 curl of the vector field F(x, y, z) = <2xy, x^2 - y^2, 3z^2>?
<0, 0, 0>
<0, 2z, 0>
<2, -2, 0>
<0, 0, 6z>
What is the limit of (e^x - 1)/x as x approaches 0?
0
1
e
undefined
What is the nth term of the geometric sequence: 3, 6, 12, 24, ...?
3^n
3^(n+1)
2^n
2^(n+1)
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)
F(b) - F(a) = f(b) - f(a)
F(b) - F(a) = ?(a to b) f(x) dx
F(b) - F(a) = 0
What is the Maclaurin series expansion of sin(x)?
x - (x^3)/3! + (x^5)/5! - (x^7)/7! + ...
x + (x^3)/3! + (x^5)/5! + (x^7)/7! + ...
1 - x + (x^2)/2 - (x^3)/3 + ...
e^x
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)
If a curve C is parameterized by r(t) = , what type of curve is it?
A line
A circle
A parabola
An ellipse
Which statement is true about the continuity of a function at a point?
The function must be differentiable at that point.
The function must have a removable discontinuity at that point.
The function must have a jump discontinuity at that point.
The function must have the same limit from the left and right at that point.
What is the derivative of ln(x) with respect to x?
1/x
x
e^x
0