Implicit differentiation

Find dy/dx by implicit differentiation of the following: x^4-y^4-x+y=10 x^3y^3-x^2y^2+y=19 Any help would be appreciated! Thank you

Calculating the critical points and sketching a function.

Let g(x) = 300-8x^3-x^4 -Find the local maximum and minimum values. -Find the intervals of concavity and the inflection points. -Use this information to carefully sketch the graph of g.

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