The limit L of a function f(x) as x approaches a exists if and only if lim f(x) as x approaches a-= lim f(x) as x approaches a+ equals L.
What is the definition of limit?
100
what is average rate of change?
What is y2-y1/x2-x1?
100
What series is
1 + X/1! + X^2/2! + X^3/3! +...
What is e^x?
100
What is the integral from a to b, of f'(x)dx equal to f(b)-f(a)?
What is the fundamental theorem of calculus?
200
d/dx (cx^n)
What is cnx^n-1?
200
A function f(x) is continuous at x=a if and only if limit f(x) as x approaches a=f(a).
What is the definition of continuity at a point?
200
Area= the integral from theta 1 to theta 2 of r^2/2 dtheta.
What is area under a polar curve?
200
What series is
1 + X + X^2 + X^3 +...
What is 1/1-X?
200
What is integral from a to b f(x)dx equals f(c)(b-a)?
What is The Mean Value Theorem?
300
d/dx (a^x), a>0
What is a^x * lna?
300
The instantaneous rate of change or derivative of a function at a point.
What is a tangent line?
300
What is the speed formula?
What is Area equals the square root of dx/dt squared plus dy/dt squared?
300
Give the series for sin(2X).
What is 2X - 2X^3/3! + 2X^5/5! - 2X^7/7! +...?
OR
What is 2X - 8X/3! + 32X/5! - 128X/7! +...?
300
If lim as x approaches a of f(x)/g(x) = indeterminate form then you can recalculate the limit of each function's derivative lim as x approaches a f'(x)/g'(x)=L
What is L'Hopital's Rule for Limits
400
d/dx (cotx)
What is -csc^2(x)?
400
The average rate of change of the function on the interval [x1, x2].
What is a secant line?
400
What is the distance traveled formula?
What is the integral from t=a to t=b square root dx/dt squared plus dy/dx squared dt?
400
What series is
X^2 - X^4/2! + X^6/4! - X^8/6! +...
What is X^2cosX?
400
By parts, by partial fractions and U-substitution are...
What are methods of integration
500
d/dx cot^-1(x)
What is (-1/1+x^2)?
500
Let f be a function which is continuous on the closed interval [a, b].
What is the definition of average value of a function?
500
dy/dt equals dy/dt divided by dx/dt
Equals 0 when dy/dt equals 0 <-->
Equals DNE when dy/dt equals 0 up and down
What is parametric slope?
500
Out of the 5 Taylor series which has an interval of convergence of [-1, 1]?
What is the inverse of tanX?
500
This method is a form of numeric integration and uses the derivative of a function, starting point and step size. Name this method and spell this man's name correctly. :)