Mems Flashcards by Analise Quinnell

Lost four values of ln function

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

How well did you know this?

Not at all

Perfectly

What is the first step to find a limit

Plug in the X value

How well did you know this?

Not at all

Perfectly

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

a. Simplify, them plug in x value

b. Find derivative of both top and bottom

How well did you know this?

Not at all

Perfectly

F’ (cosu)

-sinu•u’

How well did you know this?

Not at all

Perfectly

F’(sinu)

Cosu•u’

How well did you know this?

Not at all

Perfectly

F’(secu)

Secu tan u • u’

How well did you know this?

Not at all

Perfectly

F’(cscu)

-cscu cotu • u’

How well did you know this?

Not at all

Perfectly

F’(tanu)

Sec^2 u • u’

How well did you know this?

Not at all

Perfectly

F’(cotu)

-csc^2 u • u’

How well did you know this?

Not at all

Perfectly

0/0 means what?

Hole limit exits

How well did you know this?

Not at all

Perfectly

0/a means what

Vertical asymptote, limit DNE

How well did you know this?

Not at all

Perfectly

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

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

How well did you know this?

Not at all

Perfectly

How do you find a horizontal asymptote

Plug infinity and -infinity into highest exponent

How well did you know this?

Not at all

Perfectly

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

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

How well did you know this?

Not at all

Perfectly

Position, velocity, acceleration

S(t)=
V(t)=s’(t)
A(t)=a’(t)

How well did you know this?

Not at all

Perfectly

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

V(t)=0

How well did you know this?

Not at all

Perfectly

Speed = what?

|v(t)|

How well did you know this?

Not at all

Perfectly

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

Fg’+f’g

How well did you know this?

Not at all

Perfectly

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

Gf’-g’f
———-
G^2

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

V’=(1/3)pi (r^2 h + 2rr’h)

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

A’=8 pi r • r

d/dx lnu

u’/u

d/dx log(sub a)X

u’/(ulna)

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

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’

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

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

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

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

Arccosu or cos^-1 u

-u’/ (square root of) 1-u^2

Arctanu or tan^-1 u

u’/1+u^2

Arcsinu or sin^-1 u

u’/ (square root of) 1-u^2

What makes a function concave up?

F”>0 | Sloped increase

What does it mean if f”(x)>0

F(x) concaves up | Slopes increase

What does it mean if f”(x)<0

F(x) concaves down | Sloped decrease

What is an inflection point for R(x)

R”(x) changes signs

What os the definition of differentiable

F’ is defined with smooth gradual changes

What is the definition of twice-differentiable

F’ and f” are defined with smooth gradual changes

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

F=0 or f=DNE

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

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

Lost x values for all inflection points for graph in photos

X=2,3,5

Where is function increasing/decreasing for graph in photos

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

Where is function concave up/down in graph in photos

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

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

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

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

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

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

Number line +|- is abs max | Number line -|+ is abs min

When does acceleration increase

a’>0

d/dx u^n

nu^(n-1) • u’