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
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: 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
The slope of the tangent line
What is the derivative?
The circumference of a circle is increasing at a rate of 2pi inches per minute. When the radius is 4 inches, how fast is the area of the circle increasing in square inches per minute?
What is 8pi?
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)
If the graph of f''(x) of some function is a line of slope 4, then f could be this type of function.
What is cubic?
Express cotangent in two different forms
What is 1/tan(x) and cos(x)/sin(x)
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 equation of the line tangent to
f(x)=x^2-6x+12 at x=2
is used to approximate f(2.5), what is the approximation?
What is 3?
What is the horizontal asymptote of the following: r(x) = (3x^2 + 4)/(x^2 - 4x + 10)
What is y = 3
The 3 rules for limits to infinity
What are:
Top heavy: +/- infinity
Bottom heavy: 0
Powers equal: divide coefficients
The perpendicular line to the curve y=3-4x^3 at the point (-2,2) has this slope
What is 1/48
Water is poured into a cylindrical container at the rate of 18π cubic inches per minute. The circumference of the container is 6π inches, and the volume V of the water is given by V=πr^2h, where r is the radius, in inches, of the cylinder. What is the rate of change of the height h of the water in inches per minute?
What is 2 inches per minute
The derivative of the inverse to
f(x)=2x^3+x^2-1 at x=2
What is 1/8?