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math 5a | MATH 75 - Calculus I, Quizzes of Calculus

Class: MATH 75 - Calculus I; Subject: Mathematics; University: California State University - Fresno; Term: Spring 2015;

Typology: Quizzes

2014/2015

Uploaded on 03/06/2015

aj7pinkanrig
aj7pinkanrig 🇺🇸

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TERM 1
vertical line test
DEFINITION 1
function cannot cross a vertical line more than once
TERM 2
U
DEFINITION 2
union sign means set is togetherex: 1/x graph the domain
would have a U because small gap where not continuous but
set still together
TERM 3
e^0
DEFINITION 3
=1anything to the zero power becomes one
TERM 4
Definition of a derivative
DEFINITION 4
the derivative of f(x) with respect to x is the function f^t (x)
defined as rise/run <--> f^t (x) = f (x+h) - f(x)/ h
TERM 5
Brackets
DEFINITION 5
use them when there is a pointex: greater than or equal
toLess than or greater than would use ( )
pf3
pf4
pf5

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vertical line test

function cannot cross a vertical line more than once TERM 2

U

DEFINITION 2 union sign means set is togetherex: 1/x graph the domain would have a U because small gap where not continuous but set still together TERM 3

e^

DEFINITION 3 =1anything to the zero power becomes one TERM 4

Definition of a derivative

DEFINITION 4 the derivative of f(x) with respect to x is the function f^t (x) defined as rise/run <--> f^t (x) = f (x+h) - f(x)/ h TERM 5

Brackets

DEFINITION 5 use them when there is a pointex: greater than or equal toLess than or greater than would use ( )

Limits

is finding where a function is heading"as i approach x from the (left - or right + ) my y values are..." TERM 7

linear equation

DEFINITION 7 y = mx +bm is slope TERM 8

maximum

DEFINITION 8 highest value graph actually hits TERM 9

minimum

DEFINITION 9 lowest value graph actually hits TERM 10

Trig functions

DEFINITION 10 sin(theta) = y/rcos(theta) = x/rtan(theta = y/x

continuous definition

f(x) is continuous at x=a if the lim f(x) = f(a) x->a TERM 17

Theorem 1.5.

DEFINITION 17 a) a polynomial is continuous everywhereb) a rational function is continuous at every point where the denominator is not zero, and is discontinuous where the points at the denominator equal zero TERM 18

how to do

limits

DEFINITION 18

  1. check domain by plugging in number. is it continuous?2) can you factor or reduce to make continuous?3) if not draw the graphnote: lim v. lim v. lim x-> 3+ x-> 3- x->3are all different depending on the graph, and tell you if the graph is going towards negative infinity positive infinity, both by plugging in numbers, or 0 TERM 19

graph 18 sinx/x

DEFINITION 19 = 1 TERM 20

x/x

DEFINITION 20 when limit heading to infinity x/x =1 when x not equal to zero lim x-> infinity

Power rule

d/dx ( x^n ) = n * x^n -1put exponent in front, subtract one from exponent TERM 22

Derivative of a graph

DEFINITION 22 is the slope of the tangent line TERM 23

Product rule

DEFINITION 23 d/dx( f * g)^1 = f(x) g1(x) + f1(x) g(x)note: product rule is used to find the derivatives if it is a product (being multiplied)always find f prime and g prime first TERM 24

second derivative

DEFINITION 24 is a derivative of the first derivative (so take a derivative of whole thing, then take a derivative of what you took a derivative of) TERM 25

Definition of derivatives

DEFINITION 25 f^1 (a) = lim f(x)- f(a)/ x-a x->a = lim f(a+h) - f(a)/h n->0 = m tan (slope of a tangent line)

chain rule derivative of a

composition

used when there is a composition (something multiplied by something else) y^1 = f^1 (g(x)) * g^1(x)translatedy^1 = (derivative of the outside function) multiplied by the (derivative of inside function)