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Math 121 > Review for Test 2 > Flashcards

Review for Test 2 Flashcards

1
Q

What is the equation for the slope of the tangent line?

A

f’(a)= lim h–> 0 [f(a+h)-f(a)]/ h

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2
Q

f’ (a) is ____ of tangent line to f(x) at x=a

A

the slope

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3
Q

What is the slope of the tangent line to f(x) at x=a called?

A

The derivative

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4
Q

What is true about the limit/ slope of the tangent line if f(x)= mx+b?

A

f’(a) = m

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5
Q

What is the limit/ slope of the tangent line if f(x)= square root (x)?

A

f’(a)= 1/ 2 square root (a)

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6
Q

What is the function that gives the slope of the tangent line if you find it at a point?

A

f’(x)

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7
Q

What is the power rule?

A

f’(x)= Nx^n-1

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8
Q

What is the sum rule?

A

s(x)= f(x)+ g(x), s’(x)= f’(x)+/- g’(x)

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9
Q

What is the constant rule?

A

f(x)= c f’(x)= 0

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10
Q

True or False: Just because a function is cont, there is a derivative

A

False

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11
Q

If f(x) is not cont. is there a derivative?

A

No

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12
Q

The function is Cf(x); what is the derivative?

A

Cf’(x)

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13
Q

What is the derivative if the function is f(x)= e^x?

A

f’(x)= e^x

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14
Q

What is the product rule?

A

p’(x)= f(x)g’(x)+g(x)f’(x)

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15
Q

What is the quotient rule?

A

q’(x)= [g(x)f’(x)-f(x)g’(x)]/ g(x)^2

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16
Q

What is the reciprocal formula/ rule?

A

f(x)= 1/ g(x) —> -g’(x)/ (g(x)^2

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17
Q

What is the average rate of change?

A

delta y/ delta x—> f(x1)-f(x0)/ x1-x0

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18
Q

What is the instant rate of change?

A

f’(x0)

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19
Q

If delta x is small, then what is delta y?

A

f’(x0)deltax

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20
Q

What is the area of a circle?

A

nr^2

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21
Q

What is the marginal cost?

A

c(x+1)= c(x)+c’(x)

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22
Q

What is the equation for height?

A

s(t)+ S0+V0t-1/2(g)(t^2)

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23
Q

What is S0?

A

initial height

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24
Q

What is V0?

A

initial velocity

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25
Q

What is g?

A

gravity

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26
Q

How do you find v(t)?

A

v0-g(t)

27
Q

f’(x) of sinx

A

cosx

28
Q

f’(x) of cosx

A

-sinx

29
Q

f’(x) of tanx

A

sec^2x

30
Q

f’(x) of cotx

A

-csc^2x

31
Q

f’(x) of secx

A

tanxsecx

32
Q

f’(x) of cscx

A

-cotxcscx

33
Q

What is the rule when finding the derivative of something like f(x)= xsinx

A

1(2d)+1d(2)

34
Q

What is the chain rule?

A

f’(x)= N (stuff)^N-1(‘stuff)

35
Q

What is the derivative when y=arcsinx

A

dy/dx= (1/ (square root (1-x^2)))

36
Q

What is the derivative when y=arccosx

A

dy/dx= - (1/ (square root (1-x^2)))

37
Q

What is the derivative when y=arctanx

A

dy/dx= 1/ (1+x^2)

38
Q

What is the derivative when y=arcsecx

A

dy/dx= 1/ (x)

39
Q

What is the derivative when y=arccotx

A

dy/dx= - 1/(1+x^2)

40
Q

What is the derivative when y=arccscx

A

dy/dx=- 1/ ( x)

41
Q

What is the derivative when y=arcsin(junk)

A

dy/dx= (1/ (square root (1- (junk)^2))) x junk’

42
Q

f’(x) of f(x)= e^x

A

e^x

43
Q

f’(x), f(x)=b^x

A

b^x(lnb)

44
Q

f’(x), f(x)= lnx

A

1/x

45
Q

f’(x), f(x)=b^stuff

A

b^(stuff)lnb(‘stuff)

46
Q

f’(x), f(x) =e^junk

A

e^junk(‘junk)

47
Q

f’(x), f(x)= logbx

A

1/ (x(lnb))

48
Q

f’(x), f(x)=ln (Junk)

A

‘junk/ junk

49
Q

f’(x), f(x)=logbstuff

A

(1/ (stuff(lnb)) )’stuff

50
Q

If you have a function raised to a function you must use _____ _____

A

Log Diff

51
Q

What is ‘sinhx?

A

coshx

52
Q

What is ‘coshx?

A

sinhx

53
Q

What is ‘tanhx?

A

sec^2hx

54
Q

What is ‘sechx?

A

-tanhxsechx

55
Q

What is ‘cothx?

A

-csch^2x

56
Q

What is ‘cschx?

A

-cothxcschx

57
Q

What is the inverse arcsinhx?

A

1/ square root (1+x^2)

58
Q

What is ‘arccoshx?

A

1/ square root (X2-1)

59
Q

What is the inverse of arctanhx?

A

1/ (1-x^2)

60
Q

What is ‘arcsechx?

A

1/ [x] square root (x^2+1)

61
Q

What is ‘arccothx?

A

-1/ 1-x^2

62
Q

What is ‘arccschx?

A

-1/ [x] square root (x^2+1)

63
Q

What are the steps for solving related rate problems?

A
  1. read the problem
    2.draw a picture
  2. write an equation
  3. iimplicity differentiate
    5.plug-in known values
  4. solve
  5. answer question

Math 121 (3 decks)

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