Calc Final

1

(sinx)/x as x approaches 0

0

lim as x approaches 0 when exponent on numerator is greater than exponent on denominator

coeff/coeff

lim as x approaches 0 when exponents on numerator and denominator are the same

e^k

(1+k/x)^x

1

ln(e)

x

ln(e^x)

true

true or false: a function that is differentiable is always continuous

false

true or false: a function that is continuous is always differentiable

derivative of velocity or v’(t)

position or s(t)

derivative of acceleration or a’(t)

velocity or v(t)

antiderivative of v(t)

acceleration or a(t)

antiderivative of s(t)

velocity or v(t)

rate of change; slope

derivative

(x^n)’=nx^(n-1)

power rule

(ab)’=a\**b’+b*\*a’

product rule

(e^x)’=e^x

exponential rule

(lnx)’=1/x

natural log rule

\[a^x\]’=(x’)xa^(x-1)

chain rule

f(x)=f(xo)+f(xo)(x-xo)

local linearization

y^2=2y\*y’

implicit differentiation

short answer

related rates

lim as x approaches 1 (x^a-1)/(x^b-1)=a/b

L’Hospital

where x=0 on f’(x)

how to find critical points (max or min)

where x=0 on f’’(x)

how to find inflection points

x^3

When is a critical point not a max or min?

antidifferentiation: the area between the curve from a to b

integration

F(x)

antideriviative of f(x)

from a to b Jf(x)dx=F(b)-F(a)

Fundamental Theorem of Calculus

d/dx from a to x Jf(t)dt=f(x)

2nd Fundamental Theorem of Calculus

finding your unique solution from integration and initial value

Initial Value Problem