Limits and Continuity
Find the limit.
x-> -infinity of 2x^5 +3x^3 +x-7
What is negative infinity?
What is the meaning of a limit?
Formal Definition of the Derivative
What is lim h->0 (f(x+h)-f(x))/h?
What is the derivative of cos(3x)?
What is -3sin(3x)?
What is the limit as x->0 of sinx/x?
What is 1?
What are three examples of when should we the the limit does not exist?
When is there a jump, when is there a vertical asymptote, and when is the limit from the left is not equal to the limit from the right?
Describe the Power Rule in words? Answers may vary.
What is the derivative of csc(x)?
What is -csc(x)cot(x)?
What is the Definition of Continuity?
What is lim x->c from the left and lim x->c from the right all equal f(c).
Find the limit. What is x->0 of (1-cos(x))/x?
What is 0?
What is the derivative of e^2x?
What is 2e^2x?
What is the derivative of f(x) = e^x + csc(x)?
What is e^x + -csc(x)cot(x)?
Describe the process by which you test for continuity?
What is find the limit from the left, find the limit from the right, and find f(c). They must all be equal!
What is the Chain Rule? Answers may vary.
What is the derivative of the outer function times the derivative of the inner function?
What is the derivative of tan(sec(x))?
What is sec^2(sec(x))(tan(x)sec(x))?
What is the derivative of sin(x)?
What is cos(x)?