Unit 1
Unit 2
Unit 3
Unit 4
100
The simplified version of sec(arcsinx).
What is 1/(1-x^2)^(1/2)
100
The integral from -1 to 1 of (1/x)dx is an example of this.
What is an improper integral?
100
The three conditions for the Integral Test to hold.
What is continuous, non-increasing, and positive?
100
The parameterization of the line segment with the endpoint (-1,-3) and (4,1).
What is x = -1 + 5t, y = -3 + 4t?
200
The u substitution of the integral from 0 to 4 of x/(x+4)^(1/3)
What is the integral from 4 to 8 of (u-4)/u^(1/3).
200
The proper integral of (4x^3 - 4x^2 + 6) / (x^2 + x)
What is 4x - 8 + (8x + 6)/(x^2 + x)?
200
The type of series and convergence of the series the sum from 1 to infinity of (e^(k-1)/6^k).
What is a converging geometric series with r = e/6 < 1?
200
The formula to find the x coordinate in cartesian coordinates from polar coordinates.
What is x = rcos(theta)?
300
When R is the region bounded by the graphs of y=e^(2x), y=2, and the y-axis, the integral that correctly computes the volume of the solid formed when R is rotated around the line y=2.
What is pi times the integral from 0 to (ln2)/2 of (2-e^2x)^2 dx?
300
The partial fraction decompostition general form for the rational expression (3x-1) / (x^2(x^2+3)^2).
What is A/x + B/x^2 + (Cx + D)/(x^2 + 3) + (Ex+ F)/ (x^2+3)^2
300
The best bound on the remainder (error) for the approximation of the sum from 1 to infinity of (-1)^k/(k^2 + 1) for the 3rd partial sum approximation of the series.
What is 1/17?
300
The formula to find the theta in polar coordinates from cartesian coordinates.
What is tan(theta) = y/x?
400
The integral that gives the volume of the solid whose base is enclosed by the circle x^2 + y^2 = 1 and whose cross sections, taken perpendicular to the base and parallel to the y-axis, are squares.
What is the integral from -1 to 1 of 4(1-x^2)dx?
400
The good choice of u and dv for the integral of cosxln(sinx)dx using integration by parts.
What is u = ln(sinx), dv = cosxdx?
400
The sum of the convergent telescoping series the sum from 1 to infinity of ((3/(2k-1)) - (3/(2k+1))).
What is 3?
400
The formula for the slope of the tangent line of polar equations.
What is dy/dx = (f'(theta)sin(theta) + f(theta)cos(theta)) / (f'(theta)cos(theta) - f(theta)sin(theta))?
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