Mems Flashcards
Lost four values of ln function
Ln(-1)=DNE Ln(0)=DNE Ln(1)=0 Ln(e)=1 Ln(9)=2
What is the first step to find a limit
Plug in the X value
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
F’ (cosu)
-sinu•u’
F’(sinu)
Cosu•u’
F’(secu)
Secu tan u • u’
F’(cscu)
-cscu cotu • u’
F’(tanu)
Sec^2 u • u’
F’(cotu)
-csc^2 u • u’
0/0 means what?
Hole limit exits
0/a means what
Vertical asymptote, limit DNE
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 do you find a horizontal asymptote
Plug infinity and -infinity into highest exponent
Formula to find tangent line function and what do you plug in
Equation: y-y1=m(x-x1)
Need: x1, y1, m
Position, velocity, acceleration
S(t)=
V(t)=s’(t)
A(t)=a’(t)
What does it mean for a particle to be at rest?
V(t)=0
Speed = what?
|v(t)|
d/dx (fg) where f and g represent functions
Fg’+f’g
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’
