Calc CD Problem Sets
There aren't many of these yet...hopefully I'll add more as time goes by. I currently have no idea how to really organize these so it's just going to be a giant list...
Problem Set 1
Doing stuff with a table of f(x) and its derivative at values; derivatives of trig/inverse trig functions; volume of revolution
Problem Set 2
Separable differential equation; integration by parts; Second FTC
Problem Set 3
Function defined by a limit; tangent line; average value; volume with known cross-sections
Problem Set 4
"Re-centering" a polynomial (it's relevant to series stuff)
Problem Set 5
Geometric Series stuff
Problem Set 6
Investigating geometric series again...
Problem Set 7
Manipulating yet another geometric series...
Problem Set 8
Just your standard Taylor Polynomial problem
Problem Set 9
Taylor Polynomial problem again; a few review antiderivatives
Problem Set 10
Evaluating infinite series of constants by recognizing them
Problem Set 10-01
Taylor polynomials; approximations; error; radius of convergence; interval of convergence; geometric series; solving an equation.
Problem Set 13-01
Euler's Method; tangent line approximations; Taylor & Maclaurin polynomial approximations; finding particular solutions (some separable and some requiring the integrating factor approach--which is NOT a Calc BC topic).
Problem Set 14-01
Integral of sine squared in two ways; accumulation function, derivative; Euler's Method; Taylor Polynomial; logistic differential equation; arc length; critical points.
Problem Set 14-02
Logistic differential equation; range; Taylor polynomials; implicit differentiation--kind of...
Problem Set 16-01
Parametric equations; FTC; tangent lines; describing motion based on derivatives; finding explicit functions for x(t) and y(t).
Problem Set 16-03
Parametric equations; given graphs of dx/dt and dy/dt; first derivative; describing motion and shape of curve; speed.
Problem Set 16-04
Parametric equations; speed, velocity, acceleration; slope; position; distance traveled; describing motion.
Problem Set 16-05
Parametric equations; trapezoidal sum; tangent lines; acceleration; Euler's method; position; speed.
Problem Set 17-01
Working with dr/dt, dx/dt, dy/dt, and dy/dx. Writing tangent lines to polar curves.
Problem Set 17-02
Describing polar regions; partial fractions practice.
Problem Set 17-03
Polar practice: area, slope, dr/dt, minimums/maximums.