Limits and derivatives

Find the derivative. a) f= 4-sqrt(x+3) b) f= (x+1)/(2-x) See attachment below for additional information.

Simplifying mathematical expressions.

2^3 * 2^-4 (from Modern Engineering Mathematics 3rd Ed Ex 1.2.5.1(a))

A relative rates calculus problem regarding a kite.

A kite 100ft above the ground moves away horizontally at a speed of 8ft/sec. At what rate is the angle between the string and the horizontal decreasing when 200ft of string has been let out?

A related rates calculus problem in regards to a cone.

A waffle cone has a height of 6in with a radius at the top being 1 inch. A spherical scoop of ice cream is placed on top of the cone and melts into the cone. At a particular instant of time, the radius of the ice cream is 3/2 inch and is decreasing by 1/100 in/min. At this same time, the height of the melted ice cream in the ...continues

Working with limits.

Solve for t. lim t-->0 (sin t)^2 / (4t)^2

Ellipse, points where tangent line is vertical

Given the ellipse x2/4 + y2/9 = 1 What are the points where the tangent line is vertical? (In narrative, the problem reads: given the ellipse x squared divided by 4, plus y squared divided by 9, equals 1, what are the points where the tangent line is vertical? The problem is also attached in MS Word, in case you need it ...continues

Determining the tangential line to a curve.

The curve 2(x^2 + y^2)^2 = 25(x^2 - y^2) is called a Lemniscates. Find the tangent line at (3,1). (The problem is also attached in MS Word with the appropriate fonts)

Finding the absolute maximum and minimum values from a function.

Find the absolute maximum and absolute minimum values of f on the given interval. F(x) = sqrt(9-x^2) [-1, 2] or in other words: F(x) equals the square root of (9 minus x squared). The problem is also attached in MS word.

3x - 2 + (cos (pi x / 2) has one root

Show that the equation 3x - 2 + cos(pi x / 2) = 0 has exactly one root. (This problem may be clearer in the attached file.)

Finding the largest volume of a cylinder.

A right circular cylinder is inscribed in a sphere of radius r. Find the largest possible volume of such a cylinder.