Calculus Answers

Use an appropriate trigonometry substitution to evaluate ∫▒√(x^2+16)/x^4  dx

Evaluate the integral ∫▒〖sin〗^3 x 〖cos〗^4 xdx 

1) the equation of a curve is given as f(x)=√2x-1.find the equation of the tangent line to the graph of f(x) at x=5.

2) find the equation of the tangent line to the curve g(x)=x/x+1 at the point (2,2/3).

Express as a triple iterated integral the volume of the solid Q in the first octant bounded by the coordinate planes and the graphs of y^2+z^2=4 and 2z+x=4.Be certain to sketch the region Q for full credit

Water is being poured at the rate of 2\pi m^(3) min into an inverted conical tank that is 12-meter deep with a radius of 6 meters at the top. if the water level is rising at the rate of 1/6 m/min and there is a leak at the bottom of the tank, how fast is the water leaking the water is 6-meter deep?

The function,f: [-1,1]×[2,1] → R, defined by

f(x,y)= { x ; y is rational

{ 0 ; y is irrational

is integrable or not.

True or false with full explanation

The function,f is defined by F(x,y)=x^2+xy+y^2 is integrable over [2,1]×[1,2]. True or false with full explanation

Your classmate requests you to help him/her in understanding the solutions of the

lim

t→0

(1−cos3t)/

(3t)

= 0, via writing. How do you apply your knowledge based on what you have

learned from this module in doing the task?

1. List any TWO materials that you can include in the appendix of a long essay.
2. In a single paragraph, describe what an abstract is.

Find the area of the curve r^2 = 3-4cos^2∅, symmetrical to origin and Ox.