Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
Need help and want to know steps, plus which of the tattoo formulas i have to use if needed
Transcribed Image Text:*TATTOO"CHEAT SHEET - USE OFTEN!
youR
THE BASICS
derv.
PX) MP
CO) MC
RX) MR
X→ fcx)+y (ly CAN BE +,Ø,-)
X f'x) SLOPE(SLOPE CAN BE +,Ø,
integ.
- {0 = MAx OR MIN OR H.P.I.3)
X *f"(x) + CONCAVITY (CONCAVITY IS ,A,Ø { Bis POINT OF INFLECTION})
DERIVATIVES
PRODUCTS AND QUOTIENTS
u isA
FUNCTION,
X IS VAR.,
e AND n y= u y'= u'v -uv'
y=x^
y'= nxn-i
U AND V
youv y'- u'v+uv'
%3D
n-I
y'= nu" (u')
y=e" y'- u'e"
y=Lnu y'= 4 doutdin
y=u^
ARE
FUNCTIONS
CONSTANTS
LOGS AND EXPONENTS
y=a" y'=a"u'ına ) WHERE U
y-a* y = a*x' In a fa is const,
Fa*(1) ina
INTEGRALS
IS A FUNC,
x^dx
+K, n+-I
X IS VARVABLE
ntl
dx → U'
+k, n+-1
Un(e*) =x (SIMPLIFIED, NOT DERIVATI VE )
=X (SIMPUFIED, NOT DERIVATIVE)
y= Ju'e"dr → e" + k
in(MN) = Ln M+ inN
in (A) - LnM -UnN
in (M) = PlnM
y= logax ay =x
WHERE M
» In u +K n=-l
EN ARE
STEPS
FUNCTIONS.
(CONVERSIONS
NOT DERIVATIVĖS
1) MAKE IT PRETTY. WHICH INTEGRAL?
2) FIND U; CREATE U'
3) WE HAVE
4) MAKE IT LOOK LIKE TEMPLATE
5) PERFORM INTEGRAL
WE WANT.
CHANGE OF BASE:
y=loga x
loga
DEFINITE INTEGRALS
log X
In X
%3D
ALSO
Una
y=Jax^dx = afx°dx
Scan"
y= J(ax^+bx") dx
SFondh Fo = Fb) - Fla)
Jfandk=Fx)
%3D
%3D
a
Transcribed Image Text:3. Find y' if y(x) = (e8x – 7)*.
%3D
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