Calculus Answers

a curve y=1 - 4/(2x+1)square. the curve intersect the x- axes at A . the normal to the curve at A intersects the y- axes at B.
1) obtain expressions for dy/dx and( upper and lower limit ) |ydx
2) find showing all necessary working find all the area under the curve and normal (full)

the diagram shows a water container in the form an inverted pyramid , which is such that when the height of the water level is h cm the surface of the water is a square of side 1/2 h cm
1) express the volume of water in the container in terms of h .
[note the volume of a pyramid having a base area A and vertical height h is 1/3Ah.
water is steadily dripping into the container at a constant rate of 20 cm cube per minute.
2)find the rate in cm per minute,at which the water level is rising when the height of the water level is 10 cm.

Integrate x^2+X+5/(x^2+4)(X+1) dx

the inverse function of y=e^3x is y=1/3 lnx

Evaluate the ∫∫ y dS where S is the portion of the cylinder x2 + y2 = 3 that lies between z = 0 and z = 3.

Evaluate the ∫∫ z dS where S is the upper half of a sphere of radius 4.

Use stokes theorem to evaluate the integral

[img]https://upload.cc/i1/2020/04/16/O3K5zL.jpg[/img]



question is in picture

R=4

[img]https://upload.cc/i1/2020/04/16/pcQUg6.jpg[/img]


question in photo
R=4

A valve on a storage tank is opened for 4 hours to release a chemical in a manufacturing process. The flow rate