Definitions
The First Fundamental Theorem of Calculus states if f is continuous on the closed interval [a, b] and F' = f, then...
f(x2) - f(x1) / ( x2 - x1 )
What is average rate of change?
The derivative of sin(x) is...
What is cos(x)?
When it comes to Horizontal Asymptote, if the degree of the numerator is greater than the denominator, then the limit is...
What is UNBOUNDED?
Nxn-1
What is the power rule?
If f(x)≤g(x)≤h(x) for all numbers, and at some point x=k we have f(k)=h(k), then g(k) must also be equal to them.
What is the squeeze theorem?
lim h->0 f(x+h) - f(x) / h
What is instantaneous rate of change?
The derivative of sec(x) is...
What is sec(x)tan(x)?
If f''(x) < 0, then f(x) is concave...
What is down?
(d/dx[g(x)] ⋅ f(x)) + (d/dx[f(x)] ⋅ g(x))
What is the product rule?
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 the mean value theorem?
∫eu du
What is eu + C?
The derivative of tan'(x) is...
What is 1/(1+x2)?
If f'(x) = 0 and f''(x) >0, then (x, f(x)) is a...
What is relative minimum?
lodhi - hidlo / lo2
What is the quotient rule?
f is continuous at c if and only if...
1) f (c) is defined
2) limx->c f(x) exists
3) limx->c f(x) = f(c)
d/dx (ax)
ax lna ⋅ d/dx x
Differentiate y=esec3x
3esec3xsec3xtan3x
If f is continuous on [a,b] and differentiable on (a,b) and if f(a) = f(b), then there exists a number c on (a,b) such that f'(c) = 0.
What is Rolle's Theorem?
f'(g(x)) ⋅ g'(x)
What is the chain rule?
Let f be defined at c. If f'(c) = 0 or if f' is undefined at c, then c is...
What is a critical number of f?
Acceleration is...
a(t) = v'(t) = s''(t)
Find y' if sin(x+y) = y2cosx
y' = (y2sinx + cos(x+y)) / (2ycosx-cos(x+y))
y(t) = Cekt
What is exponential growth?
d/dx[c] = 0
What is the constant rule?