Integral : Trigonometric Substitution

int sqrt{1+x^2}/x dx

Domain of a Function and Partial Derivatives

Questions are in the attached file. For #1, find and sketch the domain of the function For #2, find the indicated partial derivatives

Functions : Radius of Convergence and Approximations

Please see the attached file for the fully formatted problems. Let f be the function defined by f(x) = sigma (starting at n=1 ending at infinity) xnnn /(3n n!) for all values of x for which the series converges. a) Find the radius of convergence of this series b) Use the first three terms of this series to approximat ...continues

Partial derivative of one function in relation of a vector

See attached file for full problem description.

Volume of a solid of revolution.

I am to find the volume of the solid obtained by revolving the region bounded by y = x^8 and y = 1 about the y = 10 axis.

The Volume of a Solid Bounded by Two Cylinders : Find the volume of the given solid, bounded by the cylinders x^2 + y^2 = r^2 and y^2 + z^2 = r^2.

Please see the attached file for the fully formatted problems. Please do #28. Find the volume of the given solid, bounded by the cylinders x^2 + y^2 = r^2 and y^2 + z^2 = r^2.

Evaluate the Double Integral

#50 Please see the attached file for full problem description.

Find the Volume of a Sphere with a Cylindrical Hole

#26 Please see the attached file for full problem description. (a) A cylindrical drill with radius r1 is used to bore a hole through the center of a sphere of radius r2. Find the volume of the ring-shaped solid that remains. (b) Express the volume in terms of height (h).

Probability : Exponential Density Function

#26 Please see the attached file for full problem description. a) A lamp has two bulbs of a type with an average lifetime of 1000 hours. Assuming that we can model the probbility of failure of these bulbs by an exponential density function with mean mu = 1000. Find the probability that both of the bulbs fail in 1000 hours. ...continues

Area of the Surface from Intersection of Two Cylinders

#22 Please see the attached file for full problem description.