# Final Review

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- Auburn University
- Calculus
- Calculus 1610
- Ghimire
- Final Review

**Created:**2014-01-31

**Last Modified:**2014-05-01

^{x}/

_{c})

^{1}/

_{C}•f(x)

^{y}= x

_{a}x=y

_{a}1 =

^{0}= 1

_{a}a =

^{1}= a

^{y}= x

_{e}x

_{e}x

_{a}(xy) =

_{a}x + log

_{a}y

_{a}(x/y) =

_{a}x - log

_{a}y

_{a}x

^{r}=

_{a}x

^{x}=

^{lnx}=

1. f(a) exists

2. lim as x tends to a exists

3. lim as x tends to a = f(a)

^{2}x

**F(x,y) = 0**is said to

**define the function y = f(x) implicitly**if, for

**x**in the domain of

**f**,

**F(x,f(x)) = 0.**Replace the

*y*with y(x) [y as a function of x]

*and then take the derivative. (Differentiate both sides of the equation with respect to "x", and then solve the equation for dy/dx).*

__f(x)__= lim

__f'(x)__

^{x→a }g(x)

^{ }

^{x→a }g'(x)

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