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Math 121 > Review for Exam 1 > Flashcards

Review for Exam 1 Flashcards

1
Q

What is the equation for slope?

A

slope= (y2-y1)/(x2-x1)

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2
Q

What is the equation of the line formula?

A

y-b=m(x-a)

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3
Q

If the you are given a rational what is the caveat about the domain?

A

The denominator of the rational can not equal zero.

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4
Q

If there is no rational and you are trying to the find the domain, what do you do?

A

You equal the equation to zero and solve for the zeros. The domain will be in between the zeros.

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5
Q

For compositions of functions what is (f o g)(x) and f(x) x g(x) essentially equal to?

A

(f(g(x))

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6
Q

sin theta when it is at 0

A

0

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7
Q

what is sin theta when is n/6

A

1/2

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8
Q

what is sin theta at n/3

A

root 3/ 2

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8
Q

what is sin theta at n/4

A

root 2/ 2

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9
Q

what is sin theta at n/2

A

1

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10
Q

what is cos theta at 0

A

1

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11
Q

what is cos theta at n/6

A

root 3/ 2

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12
Q

what is cos theta at n/4?

A

is it root 2/ 2

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13
Q

what is cos theta at n/2

A

0

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14
Q

What is tan theta at 0

A

0

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15
Q

what is tan theta at n/6

A

1/ root 3

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16
Q

what is tan theta at n/4

A

1

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17
Q

what is tan theta at n/3

A

root 3

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18
Q

what is tan theta at n/2

A
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19
Q

How do you convert a log into an exponent?

A

logb (a)= c
b^c= a

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20
Q

how do you convert a lnx to exponential?

A

lnx= y e^y =x

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21
Q

What does cos^2x+ sin^2=

A

1

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22
Q

What does tan^2x+1=

A

sec^2x

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23
Q

What does sin(2x)=

A

2sinxcosx

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24
Q

what does sin^2x=

A

1-cos2x/2

25
Q

what is sin(x+y)

A

sinxcosy+ cosxsiny

26
Q

what is cos(x+y)=

A

cosxcosy-sinxsiny

27
Q

what is cos2x

A

cos^2x-sin^2x

28
Q

what is cos^2x=

A

(1+cos2x)/ 2

29
Q

what is sinhx=

A

(e^x-e^-x)/ 2

30
Q

what is coshx=

A

(e^x+e^-x)/2

31
Q

what is tanhx=

A

(sinhx)/coshx

32
Q

what is cothx=

A

(coshx)/sinhx)

33
Q

what is sechx=

A

1/ coshx

34
Q

what is cschx=

A

1/sinhx

35
Q

Quadratic formula

A

(-b+/- root of (b^2-4ac))/2a

36
Q

if the hole is opened like o—-o then the interval is what?

A

a<x<b

37
Q

but if the hole is closed then the interval is what?

A

a</= x</= b

38
Q

distance formula?

A

square root of ((x1-x2)^2+(y1-y2)^2

39
Q

what is the equation for a circle?

A

(x-x0)^2+(y-y0)^2=r^2

40
Q

If there is a jump discontinuity does the limit exist?

A

no

41
Q

if there is a removable discontinuity is f(x) continuous at that point?

A

no

42
Q

Where is f(x) cont. at [a.b)

A

it is the cont. at the right at a

43
Q

where is f(x) cont. at (a, b]

A

it is cont left at b

44
Q

where is f(x) cont. at [a, b]

A

it is cont. at the left and right

45
Q

how do you write the slope of tangent?

A

lim b–>a = (f(b)- f(a))/ b-a

46
Q

If f(x) is sinx/x as x–> 0 what is the limit?

A

1

47
Q

True or false the denominator of denominator is really the numerator

A

True

48
Q

if f(x) is (1-cosx)/x what is the limit as x–> 0

A

0

49
Q

What is the squeeze THM or sandwich THM?

A

if g(x) /= f(x) </= h(x) then if the limit of g(x) and h(x) as x–> c is L then f(x) limit is also L

50
Q

What is the limit of P(x)/ Q(x) as it goes to +/- infinity if the degree of P(x) is less than the degree of Q(x)

A

0 C.B.B.B.T

51
Q

What is the limit of P(x)/ Q(x) if the degree of P(x) is greater than the degree of Q(x) as it approaches positive or negative infinity?

A

The limit does not exist

52
Q

What is the limit of P(x)/ Q(x) as it approaches positive or negative infinity if the degree of p(x) is equal to q(x)?

A

it is the ratio of the coefficients of the highest degree

53
Q

What is the I.V.T ?

A

If g(x) wants to equal a certain y over the interval [a, b] if the y of a and b is like Ya < the certain y < Yb then there must be a c in between [a, b] that gives that y

54
Q

If you were solving for y and you currently have x(2y+1)= 1, what is your next step?

A

2xy+x=1

55
Q

For the equation 2lnx-ln(x+4)= ln2 what is true about the possible value of x?

A

It has to be greater than 0.

56
Q

If you change the function to y= f(x)+3 what changes about the function?

A

The range

57
Q

If you change the function to y= f(x+3) what changes about the function?

A

The domain

58
Q

if you change the function f(x) to y=3f(x) what changes?

A

The range

59
Q

How do you find the x-intercept?

A

You divide the slope by the y-intercept

60
Q

Can lns or logs be negative?

A

no

Math 121 (3 decks)

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