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56 Cards in this Set
- Front
- Back
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list four values of the LN fuction |
Ln(-1)=DNE Ln(0)=DNE Ln(1)=0 Ln(e)=1 |
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What is the first step to find a limit |
Plug in the given number Lim(x->2) x+4=6 |
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0/0 means what? |
hole or limit exists |
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a/0 means what |
hole or Vertical Asymptote |
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if the first step to find a limit does not work, then what should i do? |
a. Simplify then plug it in b. derivative of top and bottom plug it in |
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for the function f(x)=x^2+x+4 over the interval (1,5) explain why there is some value of C in the interval 1<c<5 such that f(c)=30 |
f(1) = 6 f(5)=34 Since the function is continuous therer is a point below 30 and above 30. |
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How do i find a vertical asymptote? |
Plug in Infiniti and negative infiniti and to the highest exponent |
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what is the formula we use to find a tangent line to a function f(x) and what do i need to find to plug into the equation. Formula: Need: |
Formula: y-y1=M(x-x1) Need: Slope, x1, y1, and M |
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How do i find position, velocity, and acceleration functions? |
s(t) v(t)=s`(t) a(t)=v`(t) |
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what does it mean for a particle to be at rest? |
v(t)=0 |
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speed is the same as what? |
l V(t) l |
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d/dx (fg) where f and g represent functions |
fg`+ f`g |
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d/dx (f/g) where f and g represent functions |
(gf`-g`f) / g^2 |
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d/dx sinu |
cosu * u` |
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d/dx tanu |
sec^2u *u` |
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d/dx u^n |
nu^n-1 * u` |
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d/dx y^5 |
5y^4 *y` |
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d/dx secu |
secu tanu *u` |
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d/dx cotu |
(-cscu)^2 *u` |
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d/dx cosu |
-sinu * u` |
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d/dx cscu |
-cscu cotu * u` |
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given that V=(1/3)πr^2h find an equation for the rate of change of the volume if the units on the rate of change of the volume are cm^3/min. |
v`= (1/3)π ((r^2)(h`)+(2r*r^2)(h)) |
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given that A=4πr^2 find an equation for the rate of change of the area if the units on the rate of change of the area are m^2/min |
A`=4π(2r*r`) |
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d/dx lnu= |
u`/u |
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d/dx log u = b |
u`/ulnb |
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d/dx e^u |
e^u*u` |
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find dy given x^2 y + 3x = 4y^2 - 5 dx |
x^2 y` + 2xy+3 = 8y*y`
2xy + 3 = (8y*y` - x^2y`)
2xy + 3 = y` (8y-x^2)
y`= 2xy+3 8y-x^2 |
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if f and g are inverses and f(3) = 6 and f`(3) = -7 what can you tell me about g and g` |
f(x) g(x) g(6) = 3 (3,6) (6,3) g`(6) = -1/7 m=-7 m=-1/7 |
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if f(g(x)) = x then what can you tell me about a point and a slop for f(x) and g(x) |
f(x) g(x) (x,y) (y,x) m=(y/x) m=(x/y) |
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d/dx arccosu = |
-u`/sqrt(1-u^2) |
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d/dx arctan u = |
u`/1+u^2 |
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d/dx arcsinu = |
u`/sqrt(1-u^2) |
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what makes a function concave up? |
f``(x)>0 slopes increase |
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what does it mean if f``(x)>0 |
concave up, slopes increase |
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what does it mean if f``(x)<0 |
concave down slopes decrease |
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what is an inflection point for the function R(x) |
where r``(x) change signs |
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what is the definition od differentiable |
f` is defined with smooth gradual changes. |
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what is the definition of twice differentiable |
f`` is defined with smooth gradual changes |
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how do i find a critical point |
f`(x)=0 or f`(x)=dne f`= x-4 0 = 0 x-5 0 |
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what is the 2nd derivative test for relative min/max for the function g(x) |
f``(c.p.)>0 Rel min f``(c.p)<0 Rel Max |
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how do i calculate an absolute minimum/maximum on (a,b) for the function f(x) |
f(a) f(c.p.) f(b) |
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if there is only one critical point, what is the easier way to find an absolute max or min which only sometimes works |
f` number line |
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when does acceleration increase |
a`>0 |
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when does the function decrease |
f`(x) < 0 |
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what is the mean value thereom |
f(b)-f(a) b-a |
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∫ u^n du |
1/(n+1) u^n+1 + c |
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∫ 1/u |
ln lul + c |
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∫ u^-1 |
ln lul + c |
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∫ e^u |
e^u + c |
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∫ sinu |
-cosu + c |
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∫ cosu |
sinu +c |
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∫ sec^2 u |
tanu + c |
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∫ csc^2 u |
-cot u + c |
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∫ (cscu)cotu = |
cscu + c |
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∫ secutanu |
secu +c |
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find ∫ e^-4x dx |
∫ e^u du/-4 u=-4x -1/4 ∫ e^u du dx= du/-4 -1/4e u + c = (-1/4e)(-4x) + c |
