Formulas Flashcards

1
Q

Average Value Theorem

A

On interval [a, b]:
b
1 / (b - a) ∫f(x)dx
a

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2
Q

Difference Quotient (AND why/when do you use it?)

A

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

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3
Q

Riemann Sum Going to Infinity (THIS EQUALS a definite integral!!)

A

n
lim Σ f(xi) Δx
n→∞ i = 1

xi = a + iΔx
Δx = (b - a) / n

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4
Q

i (what does it equal in Riemann sum)

A

n(n + 1) / 2

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5
Q

i squared (what does it equal in Riemann sums)

A

n(n + 1)(2n + 1) / 6

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6
Q

i cubed (what does it equal in Riemann sums)

A

n^2(n + 1)^2 / 4

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7
Q

derivative of a^x:

A

lna(a)^x

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8
Q

derivative of log base a of x

A

(1/lna)(1/x)

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9
Q

derivative of the inverse function

A

1/ (f’(f-1(x))

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