Calculus Answers

Integrate with respect to x: s1 0 xdx

(a) Differentiate the equation θ = 9t² – 2t³ with respect to t.
(b) Differentiate the equation y = 3 sin 5t with respect to t.
(c) Differentiate the equation y = 2e6t with respect to t.
(d) Determine ∫▒〖x^7 dx〗.
(e) Determine ∫ (5sin 3t – e3t) dt.

5 Given that ϕ=2x^2y−xz^3 find ▽^2ϕ
6 If A=xz^3i−2x^2yzj+2yz^4, find ▽×A at point (1,-1,1).
7 Given that A=A1i+A2j+A3k and r=xi+yj+zk, evaluate ▽⋅(A×r) if ▽×A=0
8 Let A=x^2yi−2xzj+2yzk, find Curl curl A.
9 Given A=2x^2i−3yzj+xz^2k and ϕ=2z−x^3y, find A⋅▽ϕ at point (1,-1,1).
10 Find the directional derivative of ϕ=x^2yz+4xz^2 at (1,-2,-1) in the direction 2i−j−2k

1 If ϕ=2xz4−x2y, find |▽ϕ|
2 If ϕ(x,y,z)=3x^2y−y^3z^2, find ▽ϕ at point (1,-2,-1)
3 Find a unit normal to the surface x^2y+2xz=4 at point (2,-2,3)
4 Let ϕ(x,y,z)=xy^2z and A=xzi−xy^2j+yz2k,find ∂^3/∂x^2∂z (ϕA)

Let C[0,1] gave inner product defined by < f,g >= ∫ f(x)g(x)dx ; integrate from 0 to 1

Evaluate d(f,g) where g(x) = c (constant) and f(x) = e^x. Use calculus to find the smallest value of E(c) = d^2(f, g) and call the value of c at which this occurs g*(x) = c*. Calculate the values d(f, g*) and also d(f, g) for the case g = (1 + e)/2. Comment (one sentence).

hello
please i need ur help for the fractional derivative of reimann_liouville , Caputo and Grünwald-Letnikov

What is the maximum of relative extrema contained in the graph of this function? f(x)=3x^4-x^2+4x-2?

Find f(x, y) such that z = f(x, y) defines a plane and

∬ f(x,y)dA =∬ x f(x,y)dA = 0, f(1,2) = −1,

where D is the region bounded by the graphs of x + y = 3, x = 0, and y = 0.

Find f(x, y) such that z = f(x, y) defines a plane and

∬ f(x,y)dA =∬ x f(x,y)dA = 0, f(1,2) = −1,

where D is the region bounded by the graphs of x + y = 3, x = 0, and y = 0.

integration of ((sin x)^2 + 4)/((sin x)^4 +16)dx