Calculating the derivative from mathematical expressions.

Find the derivative of: f(x) = sqaure roo 4 / t^3 f(x) = 5 + 2/x + 4/x^2 f(x) = ((4x^3) - 2)/ x^4

Tan line and velocity problems

The parabola y = (x^2) + 3 has two tangents which pass through the point (0, -2). One is tangent to the to the parabola at (A, A^2 + 3) and the other at (-A, A^2 + 3). Find (the positive number) ? If a ball is thrown vertically upward from the roof of 64ft foot building with a velocity of 96 ft/sec, its height after t seconds ...continues

Integrals

(a)Let f:[a,b] ---R be continuous and f(x)>= 0 for all x an element of [a,b]. prove that if the integral between the boundaries b and a of f(x) dx =0 then f(x) =0 for all x an element of [a,b] (b)Prove that the integral between infinity and 0 of e^-st .sinat dt = a/s^2 + a^2

Integration

(a) let f:[0,1] ---R be the function f(x) = { x when x is an element of rational numbers {-x when x is not an element of rational numbers Prove that f is not integrable on [0,1] but |f| is integrable (b) Find the limit as x goes to 0 of 1/x the integral of e^t^2 dt between the boundaries 0 and x, x bei ...continues

Integrals

(a) Find the integral between o and infinity (upper)of e^-x^2 dx . Use the above to prove that T(/2)= sqare root of pi where T represents the gamma function (b) Find the integral of x^3.e^-x^2 dx between the boundaries 0 and infinity (upper) thank you

Integrals

(a)Find the integral between 0 and infinity e^-st. sinat dt (b)Let f:[0,1] --> R be the function f(x) = { x when x is an element of rational numbers {-x when x is not an element of rational numbers Prove in detail that f is not integrable on [0,1] but |f| is integrable

Optimization problems dealing with minimizing the weight of a tank.

Your iron works has contracted to design and build a 500-cubic foot, square based, open topped, rectangular steel holding tank for a paper company. The tank is to be made by welding thin stainless steel plates together along their edges. As the production engineer, your job is to find dimensions for the base and height that wi ...continues

Dissecting a trig function

Let f be the function defined by f(x)=sin squared x - sinx for 0

Having difficulty with algebra in calculus

Find intervals on which the function is: (a) increasing (b) decreasing (c) concave up (d) concave down find any (e) local extreme values and (f) inflection points for the equation y = x to the 4/5 power times(2-x)

Finding the surface area of the intersection of two cylinders.

Find the surface area of the solid that is the intersection of the two solid cylinders: x^2 + z^2 <= k^2 (x squared plus z squared is less than or equal to a constant squared) AND x^2 + y^2 <= k^2 (x squared plus y squared is less than or equal to the same constant squared) What is my f(x,y)? What are my limits of integr ...continues