CALC LOCK IN

limit definition of derivative

Alternate definition of derivative

Limit definition of integral

ln e

1

ln 1

0

ln 0

undefined

MVT (Mean Value Theorem)

EVT (Extreme Value Theorem)

Squeeze Theorem

IVT (Intermediate Value Theorem)

Definition of continuity

log e

ln

log 1

0

log 0

undefined

e^ln

cancels out

Derive sinx

cosx

Derive cosx

-sinx

Derive tanx

sec^2x

Derive cscx

-cscxcotx

Derive cotx

-csc^2x

derive secx

secxtanx

derive arcsinx

derive arccosx

derive arctanx

derive arccotx

derive arcsecx

derive arccscx

integrate sinx

-cosx+c

integrate cosx

sinx + c

integrate tanx

Integrate sec^2x

tanx + C

integrate cscx

integrate cotx

Integrate secxtanx

secx + c

integrate cscxcotx

-cscx + C

integrate lnx

xlnx - x + C

FTC part 1

FTC part 2

integrate a^x

First Derivative Test

When testing critical values, if the first derivative changes from negative to zero to positive, then that critical value is a local minimum of the function. If the first derivative changes from positive to zero of negative, then that critical value is a local maximum of the function

Second derivative test

if f'(c) = 0 and f''(c) > 0 then minimum; if f'(c) = 0 and f''(c) < 0 then maximum

arctan 1

pi/4

arctan sqrt3

pi/3

arctan(-√3/3)

pi/6

Exponential growth and decay

Logistic differential equation

Volume disk method

Volume washer method

Area under a curve

Partial fractions

Cover up rule

For a rational function

f(x)(x−a)(x−b)the fraction with numerator f of x and denominator open paren x minus a close paren open paren x minus b close paren end-fraction

𝑓(𝑥)(𝑥−𝑎)(𝑥−𝑏)

:

Set up the form:

𝑓(𝑥)(𝑥−𝑎)(𝑥−𝑏)

=𝐴𝑥−𝑎

+𝐵𝑥−𝑏

Find A: Cover up

(

𝑥

−𝑎

)

in the original expression and set

𝑥

=𝑎

in the rest.

𝐴

=𝑓(𝑎)𝑎−𝑏

Integration by parts

Taylor series

Power series

Cn(x-a)^n

a = center

cn = coefficients

x = variable

Maclaurin Series

nth term test for divergence

ratio test

p series test

geometric series test

alternate series test

alternating harmonic series

Always converges

integral test

Harmonic test

direct comparison test

limit comparison test

e^x series

sinx series

cosx series

1/(1-x) series

ln(1+x) series

arctanx series

lnx series

geometric series format

absolute vs conditional convergence

Arc length of a function

Arc length parametric

Polar and rectangular conversions

Alternating series error bound

Lagrange error bound

Vector speed

Parametric 1st derivative

parametric 2nd derivative

Polar area

Polar derivative

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