quick calc quiz 4

type 1

0/0 and in/in

type 2

0 times in and in - in

type 3

1^in and 0^0 and in^0

theorem for type 3

if y = f(x)^g(x)

then lny = g(x)ln(f(x))

d/dx (ln(kx))

1/x

d/dx(ln(g(x)))

g’(x)/g(x)

product rule

u’v+uv”

quotient rule

(u’v-uv’)/v²

natural log rules

1. ln(bx) =

2. ln(b/x) =

3. ln(x^r) =

1. ln(bx) = ln(b) +ln(x)

2. ln(b/x) = ln(b) - ln(x)

3. ln(x^r) = rln(x)

exponential growth and decay

dy/dt = ky becomes

y=Ce^kt

c = initial amount

k =growth or decay amount