Expansion of a function using Taylor's Theorem

Use Taylor's Theorem to expand the function 2(x^5) + x^2 - 3x - 5 in powers of x+1.

Double Integration

Evaluate the double integral Transform the double integral of (i) using plane polar coordinates Show that the 3 x 3 determinant See attached file:

Arc length of the curve defined by a parametric system

Find arc length of the curve defined by the following parametric system: x=cos^-1(t) (inverse cosine) y= ln t where t is less than/equal to 1, greater than/equal to (1/sqrt 2)

Applied Max-Min Problems

Please show as much work as possible, so I can understand how to solve these problems on my own. Thank you. 1. A printing company has eight presses, each of which can print 3600 copies per hour. It costs $5.00 to set up each press for a run and 10+6n dollars to run n presses for 1 hour. How many presses should be used to pr ...continues

Working with growth and decay rates and evaluating decay rate expressions.

A crude-oil refinery has an underground storage tank which has a fixed volume of 'V' liters. Due to pollutants, it gets contaminated with 'P(t)' kilograms of chemical waste at time 't' which is evenly distributed throughout the tank. Oil containing a variety of pollutants with concentration of 'k' kilograms per liter enters ...continues

Use the Maclaurin series for sinx and cosx to show that sin 2x=2 sin x cos x

Use the Maclaurin series for sinx and cosx to show that sin 2x=2 sin x cos x

Find the vertex, focus, and directrix of the parabola. Sketch its graph, showing the focus and the directrix.

1. 20x=y2 2. (x-3)squared =1/2(y+1) 3. y2+14y+4x+45=0 Find an equation of the parabola that satisfies the given conditions Focus F(0-4), directrix y=4 Find the vertices, the foci and the equations of the asymptotes of the hyperbola. 1.y2divided by 49 minus x2 divided by sixteen =1 2.x2-2y2=8 Find an equat ...continues

Integration of indefinite integrals

Evaluate the following indefinite integrals: See attached file.

vertex, focus, and directrix of a parabola.

1. 20x=y^2 2. (x-3)^2 =1/2(y+1) 3. y2+14y+4x+45=0 Find the vertex, focus, and directrix of the parabola described by the above equations.

Volume maximization : Finding the dimensions of a cylinder given the surface area.

Find the dimensions of a cylinder with a surface area of 300 cm^2 with a maximum volume.