1.1 |
Coordinate Increments and the Equation of a Line |
1.2a |
Using the vertical line test and finding the domain and range of functions |
1.2b |
Working with even and odd functions |
1.2c |
Graphing piecewise-defined functions |
1.2d |
Working with composite functions |
1.3a |
Graphing exponential functions and finding their domain and range |
1.3b |
Rewriting exponential functions with different bases and finding zeroes |
1.4 |
Graphing parameterized functions and writing parameterizations for curves |
1.5a |
Find the inverse of a function |
1.5b |
Solve exponential and logarithmic equations |
1.5c |
Determine the domain and range of logarithmic functions |
1.6a |
Working with radian measure and trigonometric values of angles |
1.6b |
Determine whether trigonometric functions are even or odd |
1.6c |
Graphing and interpreting graphs of trigonometric functions |
1.6d |
Evaluate expressions involving trigonometric functions and solve trigonometric equations |
2.1a |
Finding average and instantaneous speeds |
2.1b |
Apply the properties of limits |
2.1c |
Determine limits by substitution, tables, or graphs |
2.1d |
Finding one-sided limits |
2.2a |
Finding limits involving infinity |
2.2b |
Finding vertical and horizontal asymptotes of functions |
2.2c |
Finding power function end behavior models for functions, and identify any horizontal asymptotes |
2.3 |
Determine where functions are continuous and find/classify points of discontinuity |
2.4a |
Find average rates of change of functions over intervals |
2.4b |
Find equations of tangent and normal lines |
2.4c |
Find instantaneous rates of change |
3.1a |
Find derivatives of functions at indicated points |
3.1b |
Match graphs of functions with graphs of derivatives |
3.2a |
Determine where functions are continuous and/or differentiable |
3.2b |
Determine whether functions have corners, cusps, vertical tangents, or discontinuities |
3.2c |
Find numerical derivatives of functions at indicated points |
3.3a |
Find derivatives using the product and quotient rules |
3.3b |
Find horizontal tangents of curves with product and quotient rules |
3.3c |
Find the first four derivatives of functions |
3.4 |
Find rates of change related to velocity, including estimating from a graph |
3.5a |
Find derivatives of trigonometric functions |
3.5b |
Find velocity, speed, acceleration, and jerk of a function |
4.1a |
Use given substitutions and the Chain Rule to find derivatives |
4.1b |
Evaluate derivatives of composite functions at given values |
4.1c |
Find equations of lines tangent to curves using the chain rule |
4.2a |
Find derivatives using implicit differentiation |
4.2b |
Find slopes of curves using implicit differentiation |
4.2c |
Find equations of lines that are tangent or are normal to curves at given points using implicit differentiation |
4.3a |
Find derivatives of inverse trigonometric functions |
4.3b |
Find equations for tangent lines at indicated points of inverse trigonometric functions |
4.4a |
Find the derivative of exponential and logarithmic functions |
4.4b |
Find equations for tangent lines at indicated points for exponential and logarithmic functions |
5.1 |
Find the extreme values of functions and where they occur using critical points |
5.2a |
Find the values that satisfy the hypotheses of the Mean Value Theorem |
5.2b |
Find all possible functions with a given derivative |
5.3a |
Determine local extrema, identify any absolute extrema, or find points of inflection of a function |
5.3b |
Determine the interval on which the graph of a function is concave up or concave down |
5.3c |
Use the graph of f’ to estimate the intervals on which a function is increasing or decreasing |
5.5a |
Find linearizations of functions at given values |
5.5b |
Use linearizations to approximate expressions |
5.5c |
Find differentials |
5.5d |
Use Newton’s Method to estimate solutions |
5.6 |
Solve related rates application problems |
6.1a |
Find the exact area under a curve using finite sums |
6.1b |
Use the rectangular approximation method to approximate areas under a curve |
6.2a |
Express limits or desired quantitites as definite integrals |
6.2b |
Evaluate the integral of constant functions |
6.2c |
Use graphs of integrands and areas to evaluate integrals |
6.2d |
Evaluate the integral of a function using technology |
6.3a |
Evaluate integrals |
6.3b |
Find average values of functions |
6.4a |
Find derivatives of integrals |
6.4b |
Construct functions that satisfy given conditions |
6.4c |
Evaluate definite integrals using the Fundamental Theorem of Calculus |
6.5 |
Use the Trapezoidal Rule to approximate values of integrals |
7.1a |
Find general solutions to exact differential equations |
7.1b |
Solve initial value problems explicitly |
7.1c |
Match differential equations with the appropriate graphs |
7.1d |
Use Euler’s method to approximate the value of y |
7.2a |
Find indefinite integrals |
7.2b |
Use substitution to evaluate definite and indefinite integrals |
7.3a |
Use integration by parts to evaluate definite and indefinite integrals |
7.3b |
Use tabular integration to evaluate indefinite integrals |
7.4a |
Solve initial value problems related to exponential growth and decay |
7.4b |
Solve problems where interest is compounded continuously |
7.4c |
Find exponential functions whose graphs pass through two points |
8.1a |
Solve particle motion and projectile motion problems |
8.1b |
Solve application problems related to the integral as net change |
8.2 |
Find the areas of regions in the plane |
8.3 |
Find the volumes of solids |