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AP Calc > Mems > Flashcards

Mems Flashcards

1
Q

Lost four values of ln function

A 
Ln(-1)=DNE
Ln(0)=DNE
Ln(1)=0
Ln(e)=1
Ln(9)=2
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2
Q

What is the first step to find a limit

A

Plug in the X value

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3
Q

If 1st step to finding limit doesn’t work, what do you do?

A

a. Simplify, them plug in x value

b. Find derivative of both top and bottom

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4
Q

F’ (cosu)

A

-sinu•u’

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5
Q

F’(sinu)

A

Cosu•u’

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6
Q

F’(secu)

A

Secu tan u • u’

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7
Q

F’(cscu)

A

-cscu cotu • u’

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8
Q

F’(tanu)

A

Sec^2 u • u’

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9
Q

F’(cotu)

A

-csc^2 u • u’

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10
Q

0/0 means what?

A

Hole limit exits

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11
Q

0/a means what

A

Vertical asymptote, limit DNE

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12
Q

Function f(x)=x^2+x+4, interval [1,5], 15, can c=30?

A 
F(1)=6, f(5)=34
Since f(x) is continuous and F(1)=6 and f(5)=34 and IVT, some value of c in the interval [1,5] will be 30
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13
Q

How do you find a horizontal asymptote

A

Plug infinity and -infinity into highest exponent

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14
Q

Formula to find tangent line function and what do you plug in

A

Equation: y-y1=m(x-x1)
Need: x1, y1, m

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15
Q

Position, velocity, acceleration

A

S(t)=
V(t)=s’(t)
A(t)=a’(t)

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16
Q

What does it mean for a particle to be at rest?

A

V(t)=0

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17
Q

Speed = what?

A

|v(t)|

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18
Q

d/dx (fg) where f and g represent functions

A

Fg’+f’g

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19
Q

d/dx (f/g) where f and g are functions

A

Gf’-g’f
———-
G^2

20
Q

V=1/3(pi)r^2•h, find equation of rate of change to

A

V’=(1/3)pi (r^2 h + 2rr’h)

21
Q

A=4 pi r, fond equation of rate of change

A

A’=8 pi r • r

22
Q

d/dx lnu

A

u’/u

23
Q

d/dx log(sub a)X

A

u’/(ulna)

24
Q

Find dy/dx x^2 y+3x=4y^2 - 5

A 
1)take derivative
x^2 y’+2xy+3=8yy’
2)get y’ alone
2xy+3=8yy’-x^2 y’
3)factor out y’
2xy+3=y’(8y-x^2)
4)solve for y’
(2xy+3)/(8y-x^2)=y’
25
Q

f and g are inverses. F(3)=6, f’(3)=-7. Find g and g’.

A

F(x): (3,6) m=-7
G(x): (6,3) m=-1/7
G(6)=3, g’(x)=-1/7

26
Q

F(g(x))=x. A point and slopes for f(x) and g(x)

A

F(x): (x,y) m= ^y/^x

G(x): (y,x) m= ^x/^y

27
Q

Arccosu or cos^-1 u

A

-u’/ (square root of) 1-u^2

28
Q

Arctanu or tan^-1 u

A

u’/1+u^2

29
Q

Arcsinu or sin^-1 u

A

u’/ (square root of) 1-u^2

30
Q

What makes a function concave up?

A

F”>0

Sloped increase

31
Q

What does it mean if f”(x)>0

A

F(x) concaves up

Slopes increase

32
Q

What does it mean if f”(x)<0

A

F(x) concaves down

Sloped decrease

33
Q

What is an inflection point for R(x)

A

R”(x) changes signs

34
Q

What os the definition of differentiable

A

F’ is defined with smooth gradual changes

35
Q

What is the definition of twice-differentiable

A

F’ and f” are defined with smooth gradual changes

36
Q

How do you find a critical point for f(x)

A

F=0 or f=DNE

37
Q

List all x-values for CPs and relative extrema for f’ graph (in photos)

A

Cp: x=2,4,6
Max: x=4
Min: x=6

38
Q

Lost x values for all inflection points for graph in photos

A

X=2,3,5

39
Q

Where is function increasing/decreasing for graph in photos

A

Inc: (-infinity, 1) (6, infinity)
Dec: (4,6)

40
Q

Where is function concave up/down in graph in photos

A

Up: (2,3)(5, infinity)
Down: (-infinity,2)(3,5)

41
Q

What os the 2nd derivative test for rel max-min for function g(x)

A

Plug CPs into f”
F”(cp)>0 : rel min
F”(cp)<0 : rel max

42
Q

How do you calculate an abs min/max on [a,b] for f(x)

A

F(a), f(cp), f(b)

43
Q

If only one cp what is easier way to find abs min/max over interval [a,b]

A

Number line +|- is abs max

Number line -|+ is abs min

44
Q

When does acceleration increase

A

a’>0

45
Q

d/dx u^n

A

nu^(n-1) • u’

AP Calc (1 decks)

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