Limits
lim_(x->oo) (x-4x^6)/(2x^5+6x^6)
-2/3
What is the instantaneous rate of change of f(x)=(3x-1)^2 at x=2?
f'(2)=30
What is the formula for the average value of a function f(x) from x=a to x=b?
1/(b-a)int_a^bf(x)dx
int(sin(2x)dx
-1/2cos(2x)+c
Use Euler's Method with a step size of 0.5, starting at (1,2) to approximate f(2), for the function f whose derivative is given by
dy/dx=x-2y
1/4
lim_(x->4^-)(x^2-16)/(x-4)^2
-oo
d/dt(e^(7t)tan(7t))
7e^(7t)(tan(7t)+sec^2(7t))
If f'(x)=x and
f(2)=1, then f(4)=
7 (SPAM)
int(lnx/x)dx
(lnx)^2/2+c
The equation below will be a limacon with a loop if what condition is met? (Assume k and p are positive numbers)
r=k+p sin(theta)
p>k
(dP)/dt=0.005P(2-P/1200)
The amount of plankton in a tidepool grows logistically with a growth rate function given above. What is
lim_(t->oo)P(t)?
2400 (the A value - you have to factor out a 2 to get the correct form)
Write the equation of the line tangent to the curve below at x=4
y=sqrtx/(x-2)
y-1=-3/8(x-4)
(f(b)-f(a))/(b-a)
inte^cscx(cscxcotx)dx
-e^cscx+c
What is the radius of convergence for
sum_(n=1)^(oo) (x-2)^n/(5^nsqrtn)
x in [-3, 7)
lim_(b->oo)int_3^b1/x^3dx
1/18
f(2)=4, f'(4)=3, g(2)=4, g'(2)=-1, g'(4)=2
Find the derivative of f(g(2x)) at x=1
-6
Sand falls into a conical pile in such a way that the height of the pile increases at 3in/min. The radius of the cone is always half the height of the cone. If the volume of a cone is given by V=1/3pir^2h , what is
(dV)/dt when the height is 40in?
Include units.
1200pi "in"^3/min
int_0^6 2/(9x^2-1)dx
1/3ln(17/19)
What is the coefficient of the 8th degree term in the Taylor series for
x^2cos(x^3)
-1/2