Formulas Flashcards
Average Value Theorem
On interval [a, b]:
b
1 / (b - a) ∫f(x)dx
a
Difference Quotient (AND why/when do you use it?)
f(x + h) - f(h) / h
Can be used to calculate the slope of the secant line between two points on the graph of function f
Riemann Sum Going to Infinity (THIS EQUALS a definite integral!!)
n
lim Σ f(xi) Δx
n→∞ i = 1
xi = a + iΔx
Δx = (b - a) / n
i (what does it equal in Riemann sum)
n(n + 1) / 2
i squared (what does it equal in Riemann sums)
n(n + 1)(2n + 1) / 6
i cubed (what does it equal in Riemann sums)
n^2(n + 1)^2 / 4
derivative of a^x:
lna(a)^x
derivative of log base a of x
(1/lna)(1/x)
derivative of the inverse function
1/ (f’(f-1(x))