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CU - MATH 1300 - Study Guide

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Exam 2 Study Guide

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Variable

constant Variable

Varinbi variable

nx

(tin

initial

tial amount

I rate

onstant

TANGENT LINES EXPONENTI

Growth ower Rule Non-Power Rule Logarithmic Differentiation We also discuss several other topics like How do proteins denature when exposed to salt, ph, and heat?

1) Find duivative ( may have to

Don't forget about the age old question of Who is the first president of the philippines?

use implicit/ rt I in (b)(b*) I 1) Take in of both sides.

2) Plugin x value to get slope. I

variabl 27 Add subtract logs. 3) Exponents become coefficients. 3) Plug in coordinate to pt.kslope

If you want to learn more check out What are the three parts of parties?

e 4) Take derivatives.

formua for equation of line. 5) solve for y

to find rate, plugin a ) Plug equation back in for y.

known coordinate a

- solve. Ensure that the point ) MPLICIT DIFFERENTIATION_

EN nor s is even on the curve

LOGARITHNIC FUNCTIONS Differentiate both sides. (Assume y=f(x).

by plugging it into the C original equation, I

y = a* - loga Y = x - Isolate y' If you want to learn more check out In microeconomics what does bf stand for?

We also discuss several other topics like Where was cuneiform discovered?

In(ea) =a loga(x) + loga(y) = loc :) Plug in a courdinate to find slope of tangent line.

e incas a log(x) - logoly = m -

. Exam 2 Study Guide

Variable

constant

Vociable

variable

Variable

EXPONENTAL

Growth

1) Find derivative

use implicit/

n

initial

unate to ph.Islom

to find rate, plugin a known coordinute and

- solve.

Ensure that the point is even on the Curve Don't forget about the age old question of What are the stages of sensorimotor development?

Constant

TANGENT LINES

may have to

Power Rule Non-Power Rule Logarithmic Differentiation 1) Take in of both sides.

Dorte Per varia

variable

2) Plugin a value to get slope. I

2 Add/subtract logs. 7) Exponents become coefficients. 3) Plug in coordinate to pt. slope amount rate 4) Take derivatives.

formula for equation of line.

5) Solve for y

) Plug equation back in for y. INPLICIT DIFFERENTIATION

LOGARITHNIC FUNCTIONS

by plugging it into the 1) Differentiate both sides. (Assume y=f(x)). ( original equation,

y=a* loga y=x

2) Isolate y

In(e) = loga(x) + 10ga(y)= loga (xy)

3) Plug in a coordinate to find slope of tangent line.

e da loga (x) - loga(y) = loga (7)

4) Plug valves into point - slope formula. Horizontal Tangent Line: find where y'=0.

* Alur finding roots to an equation, find what

if found anx-value y o

d. where y'- of undefined, ones truly work - Cannot have log of neg.#* - - - - - -- ---> check it there is evena ?

Buplugging into diging

INVERSE FUNCTIONS *iff@) ab then f (b) =a. A fonction is invertible if it is one-to-one (passes horizontal line test).

If a function (ie, sinx) is not one-to-one, restrict its domain so it is able to be in vertible.

SOUP

Verhin

7 Hindu

Y value for that a-valve

Study

up

ximtition

APPLICATIONS of DERIVATIVES

Maximum Height Time of impact impact Velocity!

Original position

Solve s'(t) = 0

+ upwards for words / - down/backwards

•Solve s(t)=0

15+ Derivative - Velocity

• Use t from time of impact

Test points on either

to put in s' (t) equation.

Znd Detivatiye acceleration

side of 0. * Speeding up signs on velocity and acceleration are the same . Find wheet on left * Speed should be given in positive

Slowing Down signs on velocity + acceleration are opposite and - on right. units WC velocity only indicats direction LINEARI ZATION

If y=f(x) and fis differential, then

dx is independent variable and dy

$(x) f(a) + f'(o)(x-a) to f(x) at xsa is... when x is near a.

described as dy = f'(x) dx.

f'(x) = RELATIVE ERROR (think of error as your known iekte) RELATED RATES dx error valve calculated

o Draw label diagram. * what it should be regularly (pvt * in original - NOT derivative) Identify known and unknown rates. # often convert to a puunt*

wite an equation selating known/unknon n. © Tako duivative.

Substituke numbers into duivative.