final cal 1

Using the graphs of the function f and g, evaluate the following limits.

1. Find what the limit is approaching, divide the two numbers and get the limit.

Find the following limits algebraically(analytically).

1. Test the approaching number to see if it works.

2. If the number doesn’t work, attempt to rewrite the problem and solve again.

3. Watch out for special limits like 1-cosx/x = 0 and 1/0 = infinity.

4. If from a direction, test for positive or negative infinity.

Find an equation of the tangent line to the graph of the given point.

1. Find the derivative.

2. Find Mtan by setting the x value to the derivative.

3. Use the given points and found mtan in y = mx+b to find b.

Implicit differentiation.

1. Take derivative of both sides with respect to x

2. Only put y’ IF the variable with why was derived.

3. Solve from there for y’.

Logarithmic Differentiation:

1. Take the ln of both sides. Use log rules to rewrite problem if needed.

2. Take the derivative of both sides and solve like normal.

A-E problems:

1. Find the critical numbers from setting the derivative or denominator to 0.

2. Find inc or dec using number line and testing interval values for positive or negative.

3. Plug in critical numbers to the original function to find relative extrema.

4. Repeat with second derivative and find the second pair of critical values.

5. Plug in the second derivative critical numbers into the original function for the points of inflection.

6. Use number line and table to find the concavity of the graph. + = up and - = down

Infinite limits

1. Take the largest terms and compare to find the limit.

2. Substitute in infinites if needed to test for positive or negative.

Indefinite integral:

1. Rewrite and use basic rules to solve.

2. If that doesn’t work, use U-sub. May need to long division.

3. If U-Sub does not work, check for trig identities, may need to complete the square or split integral.

Definite Integral:

1. Rewrite and use basic rules to solve.

2. If that doesn’t work, use U-sub. May need to long division.

3. If U-Sub does not work, check for trig identities, may need to complete the square or split integral.

4. Evaluate at a to b, with f(b) - f(a) and solve.

Sketch and shade graphing:

1. Use equations to graph or plug into calculator

2. Use Area = integral of low x to high x (f(Bigger/Right) - f(Smaller/Left))

3. Y graphs don’t work on calculator.