Calc 2 Exam 1 Flashcards
(52 cards)
0
Q
d/dx (lnx) =
A
1/x
1
Q
What is the inverse of:
Y=f(x)
A
x=f^(-1)(y)
2
Q
Integrate 1/x
A
ln(t)
3
Q
Quotient Rule:
f(x)/g(x)
A
f’(x)g(x) - g’(x)f(x)
Divided by…
[g(x)]^(2)
4
Q
e^(x+y)
A
(e^x)(e^y)
5
Q
e^(x-y)
A
(e^x)/(e^y)
6
Q
e^lnx
A
x
7
Q
ln(e^x)
A
x
8
Q
y = a^x
A
y = e^(xlna)
9
Q
Derivative of…
a^(x)
A
a^(x)lna
10
Q
log(a)x
A
lnx/lna
11
Q
Differentiate…
log(a)x
A
1/(xlna)
12
Q
limit of lnx as x glues to infinity
A
Infinity
13
Q
Limit of lnx as x approaches 0+
A
negative infinity
14
Q
Limit of e^x as x approaches infinity
A
Infinity
15
Q
Limit of e^x as x approaches (-) infinity
A
0
16
Q
Exponential function for population
A
P(t) = P(0)e^(kt)
17
Q
Money increase function
A
A(t) = A(0)(1+percent in decimal form / k)^(years x k) K= number of months... Years... Days in a year
18
Q
Derivative of…
arccos(x)
A
(-1)/[(1-x^2)^(1/2)]
19
Q
Derivative of…
arctan(x)
A
(1)/(1+x^2)
20
Q
Derivative of…
arcsin(x)
A
(1)/[(1-x^2)^(1/2)]
21
Q
Domain of secx
A
[0,pi/2) [pi,3pi/2)
22
Q
Domain of sinx
A
(-pi/2,pi/2)
23
Q
sinh(x)
A
(e^x - e^-x)/2
24
cosh(x)
(e^x + e^-x)/2
25
e^(2x)
e^(x^2)
26
What would you use if limit is...
| 0/0
L'Hopitals Rule
27
What would you use if limit is...
| infinity/infinity
L'Hopitals Rule
28
What would you use if limit is...
| 0(infinity)
algebra
29
What would you use if limit is...
| infinity(infinity)
algebra
30
What would you use if limit is...
| 1^(infinity)
ln / log
31
What would you use if limit is...
| 0^0
ln / log
32
What would you use if limit is...
| infinity^0
ln / log
33
Integration by parts function
uv - integrate(v)du
34
cos^2(x) + sin^2(x)
1
35
sin(x+y)
sinx cosy + cosy siny
36
cos(x+y)
cosx cosy - sinx siny
37
sin(2x)
2sinxcosx
38
cos(2x)
1 - 2sin^2(x)
39
cos^2(x)
(1 + cos2x)/2
40
sin^2(x)
(1 - cos2x)/2
41
tan^2(x) + 1
sec^2(x)
42
Integrate secx
ln |secx + tanx|
43
Integrate 1/(x^2 + a^2)
(1/a) arctan(x/a) + c
44
How would you use trig substitution?
You would make x equal a trig value which you can switch and bring out of a square root.
45
Volume of a cylinder
2(pi)rh(change in r)
46
Cylinder method
Integrate from a to b
| 2(pi)xf(x)dx
47
Work in filling water
Integrate distance x gravity x density x area dx
| -integrating (work(force(mass(volume))))
48
Arc Length
```
Integrate from a to b:
Square root (1 + [f'(x)]^2)dx
```
49
Hooked Law
F = kx
50
a^x
e^(xlna)
51
loga(x)
lnx/lna
