Differentiation
f(x)= 3e2x
g(x)= x2-2x
h(x) = f(x) * g(x)
Derive h(x). Simplify
6e2x(x2-x-1)
f(x) = 2/(4x+7)
Antiderive f(x).
1/2 * ln|4x+7| + C
f(x) = 1/2 * csc(2x)
Derive f(x). Simplify
-csc(2x)cot(2x)
f(x) = 2e2x
Find the area under the curve from x=0 to x=1/2.
e-1
f(x) = (4x3-2x2+5) / (6x2-10x3-5x)
Find the limit of f(x) as x approaches infinity
-2/5
A circle's radius is changing at a rate of 4 m/s. Find the rate of change of the area when the radius is 2 m.
A=pi * r2
CALCULATOR ALLOWED
16pi
f(x) = ln(8x5+4x3+12x2+7x+234)
find the limit of fl(x) as x approaches infinity
0
f(x) = cot(x/2)
Antiderive f(x).
2 ln |sin(x/2)| + C
The acceleration of a particle is given by the function a(t)=3t2+7. Find the position function of the particle given that its initial velocity is 10 m/sec and an initial height of 80m.
s(t)=.25t4+3.5t2+10t+80?
f(x) = x2-3x-10
g(x) = -x2+5x+14
Find the area between the curves.
CALCULATOR ALLOWED
170.667
f(x) = arctan(4ex/2)
Derive f(x). Simplify.
(2ex/2)/(1+16ex)
f(x) = 4 sec(2x) dx
Find the area under the curve from x=0 to x=pi
0
The acceleration function for a given object is 3t2-1/3*t3. Find the total distance traveled by the object from 0 to 3.
16.2
Find the volume of the region bounded by y=x2, x=2, and y=0, rotated around y axis.
CALCULATOR ALLOWED
8pi
f(x) = x(4x+1)1/2
Derive f(x). Simplify.
(6x+1) / (4x+1)1/2
S dx / (4-9x2)1/2
Integrate.
1/3 * arcsin(3x/2) + C
f(x) = 8x3
g(x) = sin(pi*x)
Find the volume of the shape created when revolving the area between the two curves around the line y=1, for x >= 0.
CALCULATOR ALLOWED
.208pi or .654