Limits
limx->9(x2)
What is 81?
The derivative of x2
What is 2x?
The antiderivative of -csc2x
What is cotx?
If f is continuous on the closed interval [a,b], f(a) β f(b), and k is any number between f(a) and f(b), then there is at least one number c in [a, b] such that f(c) = k
What is Intermediate Value Theorem?
d/dx (xn) = nxn-1
limx->3[(x2-3x) / (x-3)]
What is 3?
The derivative of 4x3
What is 12x2?
The antiderivative of 1/x.
What is ln|x|?
If a function is continuous on a closed interval [a,b], then the function must have a maximum and a minimum on the interval.
What is Extreme Value Theorem?
d/dx (f(x)g(x)) = f(x)g'(x)+g(x)f'(x)
What is Product Rule?
limx->inf[(5x-3) / (3-2x)]
What is -5/2?
The derivative of (3x2-x)(4+x2).
What is (3x2-x)(2x)+(4+x2)(6x-1)?
or (simplified)
What is (12x3-3x2+24x-4)?
int0->1[2x2-x3]dx
(integral from 0 to 1)
What is 5/12?
If a function f is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists a point c in the interval (a,b) such that f'(c) is equal to the function's average rate of change over [a,b].
What is Mean Value Theorom?
d/dx (f(x)/g(x)) = (g(x)f'(x)-f(x)g'(x)) / (g(x))2
AKA
LdH-HdL / L2
What is Quotient Rule?
limx->inf[4x + 3/x2]
What is infinity?
The derivative of secx.
What is secxtanx?
int [x2(x3+5)4] dx
What is (1/15)(x3+5)5 + C?
If f(x) is continuous on [a,b] and differentiable on (a,b) and if f(a) = f(b), then there exists at least one number c on (a,b) such that f'(c) = 0.
What is Rolles' Theorem?
limx->c(f(x)/g(x)) = limx->c(f'(x)/g'(x))
What is L'HΓ΄pital's rule?
limx->5[(x2-25) / (x2-4x-5)]
What is 10?
The derivative of (2cos2x)/(3sinx).
(Simplification not necessary, just use quotient rule)
What is [(3sinx)(-2sin2x)-(2cos2x)(3cosx)] / (3sinx)2?
The antiderivative of 1 / β1-xΒ²
What is arcsinx?
f(x) = int_a->x f(t) dt
(the integral from a to x)
What is the Fundamental Theorem of Calculus?
d/dx [π(π(π₯))] = πβ² (π(π₯)) β πβ² (π₯)
What is the Chain Rule?