Final exam Flashcards

1
Q

2.1

average velocity

A

change in distance/ change in time

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2
Q

2.1

instantaneous velocity

A

1st derivative of a position equation

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3
Q

acceleration

A

2nd derivative of position function

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4
Q

2.1

slope using two points

A

Y2-Y1/X2-X1

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5
Q

Point slope form

A

(Y-Y1)=m(X-X1)

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6
Q

2.2

If a limit as X approaches 3+ = 4 and the limit as X approaches 3- = -4 does the limit exist?

A

no the limit does not exist, must agree on both sides

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7
Q

definition of a vertical asymptote

A

limit as x approaches a of f(x) = positive or negative infinity

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8
Q

a non zero number/ 0 =

A

+- infinity

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9
Q

2.5

what are the three points needed for a function to be continunous?

A
  1. f(a) is defined
  2. limit as x approaches a = f(a)
  3. the limit as x approaches a exsits (cant be one sided)
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10
Q

domain of polynomials

A

All reals

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11
Q

domain of a rational function

A

where the denominator does not = 0

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12
Q

domain of trig functions

A

all reals

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13
Q

domain of exponential functions

ex: e^x, 2^x, 7^x

A

all reals

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14
Q

domain of logarithmic functions

ex: ln, log

A

(0, infinity)

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15
Q

2.5

Intermediate value theorum

A

on a closed interal from [a,b] a continuous function will have a value for f(c) somewhere bc/ it is continuous

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16
Q

domain of odd and even root functions

A

odd (all reals)
even [o, infinity)

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17
Q

2.7

definition of a derivative

A
  • lim as h approaches 0 f(a+h) -f(a)/h = f(x)-f(a)/x-a
  • the slope of the tangent line
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18
Q

2.8

What does it mean to be differentiable?

A

if a function is differentibale at a point that means the derivative exists there and it is continuous

not differentiable where the derivative cannot exist

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19
Q

2.8

True or false? if x= a is cont then f is differentiable at x=a

A

false, you cant swap the sentence and still have it be true

20
Q

3.1

derivative of b^x=

A

b^x *ln(b)

21
Q

3.5

Implicit differentation

A

taking the derivative on both sides with the assumption that y is a function/ y= f(x)

22
Q

3.10

differentials

A

dy=f’(x)* dx

use this for measurement error problems

23
Q

3.10

surface area of a cube

24
Q

4.1

extreme value therorum

A

if f(x) is continous on a closed interval then f(x0 has an absolute max and min on that interval

on closed intervals you can choose the ends

25
# 4.1 the point is a critical point if...
f'(c) = 0 or f'(c) DNE
26
# 4.1 if f(x) has a local max or local min at x=c then f'(c) = 0 or f'(c) DNE
fermats theorum | CRITICAL POINT DOES NOT =. LOCAL MIN/MAX
27
# 4.2 Rolles theorum
1. f(a) =f(b) 2. f(x) is cont on (a,b) 3. f(x) is differentiable on (a,b) - f'(c) = 0 | use to prove at most one solution
28
# 4.2 Mean Value Theorum
1. f is cont on (a,b) 2. f is differentiable on (a,b) - f'(c) = f(b)-f(a)/b-a | average rate of change from a to b
29
# 4.3 Inflection points
where concavity changes from up or down or vice versa
30
# 4.4 what should you do if you get the indeterminate form 0/0 or infinity/infinity
take the derivative of the top and bottom separatley | L'hopital
31
# 4.4 What should you do if you get the indeterminate form 0 * infinity
f(x)/ (1/g(x))
32
# 4.4 what should you do if you get the indeterminate form infinity - infinity
find a common denominator or factor
33
# 4.4 what should you do if you get the indeterminate form of 0^0, infinity^0 or 1^infinity
e^ln(fx) and bring the limit up
34
# 4.5 how do you find the x and y intercepts of a function?
x int: 0= f(x) y-int: y= f(0)
35
# 4.5 how do you determine symmetry for a function?
odd symmetry: f(-x)= -(f(x)) even: f(-x)=f(x)
36
# 4.9 Never forget to add what after the most general antiderivative?
+ C
37
Derivative of a log | log(x) base a
1/x*ln(a)
38
# 5.1 What does it mean to use right end points?
to use the right most values, leaving out the lowest value - ex: of your points are 0, 1/2, 1 and 3/2 for right most you wouldnt use 0
39
# 5.2 What does it mean to use leftmost end points?
use the left most values and the lowest value - ex: if your values are 0,2,4,6 then you wouldnt use 6
40
# 5.1 How do you find your change in x? | [a,b] w/ n number of rectangles
b-a/n
41
# 5.3 What does the Fundamental theorum of calculus let you do?
if f is cont on [a,b] then the intetral from a-b on f(x) is any antiderivatve F(b)- F(a)
42
definition of a absolute maximum
x=b is a local max of f(x) if f(b)> f(x) for any x near b
43
definition of an absolute minimum
x=a is an absolute minimum if f(a)
44
# 5.3 FTC pt 2
if f(x) is cont then the integral from a to b is = any antiderivative F(b)-F(a)
45
# 5.5 What should you never do when using the u sub rule for integrals?
u=x | it wont do anything