Calc 1 formulas

good luck on the final!

Limit (informal)

Limit (formal)

Continuity

1. f(c) is defined

2. lim x→c f(x) exists

3. lim x→f(x) =f(c)

Derivative

Concavity

The Fundamental Theorem of Calculus

Tangent line

Point Slope Formula

Chain rule

Quotient rule

Product Rule

Power rule

Infinite limits

Trig derivatives

Trig anti-derivatives

Max extrema

Min extrema

extreme value theorem

Mean value theorem

Rolles’s theorem

quadratic formula

Power Rule (Anti Derivatives)

Upper/right sum

Lower/left sum

Trapiziod sum

Midpoint rule formula

Limits of lower and upper sums

Special trig limits

sinax/bx= a/b,

sinax/x=a

tanx/x=sinx/cosx,

only works when x→0

Squeeze theorem

if h(x)≤ f(x) ≤ g(x) for all x in an open interval containing c, except possibly at c itself.

As x equals c, h(x) and g(x) have the same limit, then if f(x) exists, it is equal to L.

must have the same limit

Derivative of sinx

cosx

Derivative of cosx

-sinx

Derivative of tanx

sec²x

Derivative of secx

secxtanx

Derivative of cotx

-csc²x

Derivative of cscx

-cscxcotx

Antiderivative of sinx

-cosx +C

Antiderivative of cosx

sinx +C

Antiderivative of