calc

Linearization formula

L(x) = f(a) + f'(a)(x-a)

Velocity u

m/s

acceleration units

m/s^2

Variable base, constant exponent

n(x^n-1

moving forward

velocity>0

moving backward

y<0

at rest?

y=0

Linear approximation error

| actual - approx | <0.5

cos^-1x

-1/sqrt(1-x^2)

csc^-1(x)

-1/xsqrt(x^2-1)

constant base constant exponent

0

cot^-1 x

1/(1+x^2)

tan^-1x

1/(1+x^2)

sin^-1(x)

1/sqrt(1-x^2)

ln u

1/u times derivative of u/x 1/numerator times derivative numerator - 1/denominator times derivative of denominator

derivative of ln |x|

1/x

ln x

1/x

log b x

1/x ln b times derivative of x

sec^-1 x

1/xsqrt(x^2-1)

dv formula

4pir^2 * dr

volume of sphere

4πr^2 * dr/dt

fi4rst five seconds

ABSOLUTE VALUE 0->1; f(1)-f(0) 1->3; f(3)-f(1) 3->5;f(5)-f(3) add differences

speeds up?

Direct relationship bw acceleration + velocity

population growth

P0(e^k*0)

Dx formula

X2-X1; plug into dy formula

law of cooling

Y0e^kt

Dy formula

Y2-Y1; plug into dy formula

Constant base, variable

b^x(ln b)(x')

Marginal cost?

dericative of C/derivative of x

dy formula for differentials

f'(x) dx

average density formula

f(x2)-f(x1)/x2-x1

speeds down?

inverse relationship bw acceleration and velocity