Pre-Calculus
Evaluate: csc(pi/6)
What is 2
What is the limit as x approaches a number if the function oscillates around the number.
What is undefined
The following are two conditions for continuity:
A. f(a) is defined
B. the limit as x approaches a of f(x) exists
What is the third condition?
What is the limit as x approaches a of f(x) equals f(a)
What does the second derivative indicate?
What is acceleration OR what is concavity
Integral of sec^2(x)
What is tan(x)+C?
Evaluate: arctan(1)
What is pi/4
The three situations in which a limit fails to exist
one-sided limits are not equal
limit does not approach a finite value
oscillating function
Name the three ways that a function can fail to be differentiable
What is A. A corner, B. A discontinuity, C. A vertical tangent
What is the derivative?
A visual representation of the set of solutions to a differential equation
What is a slope field?
True/False: If f(a) is undefined, then the limit as x approaches a will also be undefined.
What is False: Not Necessarily
Evaluate: d/dx[3pi^2+e]
What is 0?
The Mean Value Theorem (state it)
A function that is continuous and differentiable on (a,b) then there exists a number c such that
f'(c)=(f(b)-f(a))/(b-a)
The definition of a derivative in limit notation
What is the limit as x ->a of (f(x)-f(a))/(x-a)
or
the limit as h->0 of (f(x+h)-f(x))/h
Evaluate: lim as x approaches a of c
What is c
If f(x)=7x-3+lnx, then f'(1)=
What is 8?
What is the 27th derivative if cos(x)?
What is sin(x)
If the graph of f'''(x) of some function f is a line of slope 2, then f'(x) could be what type of function?
What is a cubic function?
The 3 rules for limits to infinity
What are:
Top heavy: +/- infinity
Bottom heavy: 0
Powers equal: divide coefficients
What is a critical number?
What is a number that makes the derivative equal to zero or undefined.
How do you determine where a function has a relative maximum?
What is where the derivative of the function changes from positive to negative OR check critical points and see where the second derivative is negative
The indefinite integral of (3-2x)^8
What is (-(3-2x)^9)/18 +C?