Typical material covered in Calculus 1 course?

Question

I have a copy of Larson's Calculus: early transcendental functions, 2nd edition. I was wondering what material I would need to cover to have the equivalent of a Calculus 1 course at a University. I plan on taking the clep exam for Calculus 1.

Answer 1

So most semester-long university Calculus 1 courses cover up through basic integration techniques (chapters 1,2,3,4,5, and 8 in Larson's book), so that's what I would recommend. From chapter 8, I'm mainly looking at the sections on integration by parts and L'Hospital's rule.

Although, I'm not sure what exactly is covered in the CLEP exam, so you might also want to study chapters 6 and 7.

Note: this is just my experience from talking to friends from high school that went to universities all over California, so you'll want to take others' advice as well.

Answer 2

I'm just finishing a Calculus 1 class this semester and here's the main types of problems we have learned to solve:

How to take $ n $ number of derivatives of a function using the chain rule, the power rule, the product rule, and the quotient rule. Using the derivative to find the max and min of a function.

Problems involving the tangent line to a curve and finding the equation of a tangent line and a normal line (line perpendicular to the tangent line).

Evaluating limits involving infinity, and 0, and indeterminate forms using $L'Hospitals$ rule.

Differential equations and problems using differential equations.

The Mean Value Theorem and problems involving it.

We also learned implicit differentiation, and along with this we learned how to solve related rates problems (as the diameter of a snowball decreases as it melts, how much does it's circumference decrease).

We learned about second and third derivatives and concavity and how to find inflection points.

With all these problems you will need to know how they relate to trigonometric functions($ cosx, sinx, tanx$, etc), functions involving $ e^x $ and $ ln x $.