Calc 2 Exam 1 Flashcards
d/dx (lnx) =
1/x
What is the inverse of:
Y=f(x)
x=f^(-1)(y)
Integrate 1/x
ln(t)
Quotient Rule:
f(x)/g(x)
f’(x)g(x) - g’(x)f(x)
Divided by…
[g(x)]^(2)
e^(x+y)
(e^x)(e^y)
e^(x-y)
(e^x)/(e^y)
e^lnx
x
ln(e^x)
x
y = a^x
y = e^(xlna)
Derivative of…
a^(x)
a^(x)lna
log(a)x
lnx/lna
Differentiate…
log(a)x
1/(xlna)
limit of lnx as x glues to infinity
Infinity
Limit of lnx as x approaches 0+
negative infinity
Limit of e^x as x approaches infinity
Infinity
Limit of e^x as x approaches (-) infinity
0
Exponential function for population
P(t) = P(0)e^(kt)
Money increase function
A(t) = A(0)(1+percent in decimal form / k)^(years x k) K= number of months... Years... Days in a year
Derivative of…
arccos(x)
(-1)/[(1-x^2)^(1/2)]
Derivative of…
arctan(x)
(1)/(1+x^2)
Derivative of…
arcsin(x)
(1)/[(1-x^2)^(1/2)]
Domain of secx
[0,pi/2) [pi,3pi/2)
Domain of sinx
(-pi/2,pi/2)
sinh(x)
(e^x - e^-x)/2
cosh(x)
(e^x + e^-x)/2
e^(2x)
e^(x^2)
What would you use if limit is…
0/0
L’Hopitals Rule
What would you use if limit is…
infinity/infinity
L’Hopitals Rule
What would you use if limit is…
0(infinity)
algebra
What would you use if limit is…
infinity(infinity)
algebra
What would you use if limit is…
1^(infinity)
ln / log
What would you use if limit is…
0^0
ln / log
What would you use if limit is…
infinity^0
ln / log
Integration by parts function
uv - integrate(v)du
cos^2(x) + sin^2(x)
1
sin(x+y)
sinx cosy + cosy siny
cos(x+y)
cosx cosy - sinx siny
sin(2x)
2sinxcosx
cos(2x)
1 - 2sin^2(x)
cos^2(x)
(1 + cos2x)/2
sin^2(x)
(1 - cos2x)/2
tan^2(x) + 1
sec^2(x)
Integrate secx
ln |secx + tanx|
Integrate 1/(x^2 + a^2)
(1/a) arctan(x/a) + c
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.
Volume of a cylinder
2(pi)rh(change in r)
Cylinder method
Integrate from a to b
2(pi)xf(x)dx
Work in filling water
Integrate distance x gravity x density x area dx
-integrating (work(force(mass(volume))))
Arc Length
Integrate from a to b: Square root (1 + [f'(x)]^2)dx
Hooked Law
F = kx
a^x
e^(xlna)
loga(x)
lnx/lna
