Derivatives
Integrals
Differential Equations
Miscellaneous
Series
100
d(x2)/dt
2x
100
Integral of 3x2
x3 + c
100
dy/dt=5, y(0)=y0
y=5t
100
What does it mean when a two sided limit is undefined?
The one sided limits from either side do not equal each other.
100
How does one construct a Taylor Series for f(x) about a?
f(a)+f'(a)(x-a)+f''(a)(x-a)2/2...+f(n)(a)(x-a)n/n!
200
d(e5x)/dx
5e5x
200
Integral of 5dx/x
5lnx + c
200
dy/dt=ky, y(0)=y0
y=y0ekt
200
What is the derivative of f(g(x)) for x=5? g(5)=1, f'(1)=10, g'(5)=6
16
200
What are the first four nonzero terms of the maclaurin series for sin(x)
x-x3/3!+x5/5!-x7/7!
300
d(arctanx)/dx
1/(1+x2)
300
Integral of esinxcosxdx
esinx+c
300
dT/dt=-k(T-Ts), T(0)=T0
T(t)=Ts+(T0-Ts)e-kt
300
Name a type of undefirentiable function
Corner or cusp or vertical tangent or discontinuity
300
What are the first four nonzero terms of the maclaurin series for cos(x)
1-x2/2+x4/4!-x6/6!
400
d3(xsinx)/dx3=
-3sin(x)-xcos(x)
400
Integral of 1/(x2+25)
arctan(x/5)+C
400
dP/dt=kP/m(m-P)
m/(1+Ce-kt)
400
What is the alternate definition of a derivative?
limx-a(f(x)-f(a))/(x-a)
400
What function is represented by the series 1+x+x2/2+x3/3...+xn/n
ex
500
y=sec(sec(sec(x))). dy/dt=?
0
500
integral of ln(x)dx
xlnx-x+C
500
V-q/C-Rdq/dt=0, V,C, and R are constants
q=CV(1-e-t/RC)+c
500
What is the volume of the 3D figure obtained after rotating the region bounded by y=sinx, y=cosx, and x=0 about the line y=-1.
fnInt(π((cos(x)+1)2-(sin(x)+1)2)dx,x,0,π/4)=4.173.
500
What is the interval of convergence for Σ(-1)n+1n100xxn
(-1,1]
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