Derivatives
d/dx sin(x³-4)
3x2cos(x3-4)
Lim x→∞ ex/-x
-∞
∫sinxdx
-cosx+c
A conical reservoir is being filled at a rate of pi ft/s. The reservoir has a radius of 6 feet at the top and a depth of 12 feet. Find the rate at which the height is changing when the depth is 6 feet.
1/9
Find the area of the region bounded by y=x2-3 and y = x/2
13/3
d/dx x4-3(12x-3)2
4x3-864x+216
Lim x→-∞ (ex-x5)/(sinx+e-x)
0
0∫4 x/4x
1
Build a rectangular pen with three parallel partitions using 500 feet of fencing. What dimensions will maximize the total area of the pen?
125x50
Find the volume of the solid of revolution around the x-axis
1024π/5
d/dx 1/(log3x)
-1/(xln(3)log32(x)
Lim x→∞ (ex-e-x)/6x
∞
-8∫8 x3dx
0
We want to construct a box whose base length is 3 times the base width. The material used to build the top and bottom cost $10/ft2 and the material used to build the sides cost 6/ft2. If the box must have a volume of 50 ft3, determine the dimensions that will minimize the cost to build the box.
4.71 x 1.88
Find the average rate of change of 3∫7 (3x)/(4x2-2)dx
-129/3298
d/dx (1+sinx)/(3+cosx)
(1+3cosx+sinx)/(3+cosx)2
Lim x→∞ xsin(1/x)
1
∫secxtanxdx
secx+c
ERROR
ERROR
A particle travels according to the following velocity function v(t)=3t2-12, what is the total distance traveled from t =1 to t = 5
76
d/dx (2x√x²+1)/(x+1)2/3
(8x3+12x2+2x+6)/(3(x+1)5/3(x2+1)1/2
Lim x→∞ x/√1+x
∞
0∫b 3x9+3dx
((3b10)/10) + 3b
A person in a rowboat two miles from the nearest point on a straight shoreline wishes to reach a house 6 miles farther down the shore. If the person can row at a rate of 3 mph and walk at a rate of 5 mph. How far away from the house should the person in the rowboat land on the shoreline?
4.5 miles away from the house
Find the volume of a solid bounded by y = 2√x - 4, y + 3x2-6 and the y-axis when rotated around y=-1
421∏/30