h(x, y) = (2x sin(y)-e) i + ² cos(y) j r(u) = cos(u)i +2uj u = [0, π] E

Q: X = cos 2t, y = cos t, 0 <t< n

A: given x=cos2t and y=cost interval 0&lt;t&lt;π  dx/dt =d/dt(cos2t) dx/dt=-2sin2t And dy/dt=d/dt(cost)…

Q: Find f. f "(x) = 7 + cos(x), f(0) = -1, f(7x/2) = 0 %3D %3D f(x)

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: (a) fr = 4xz2, fy = yz and f; = xz 2 sin (x), fy = cos(x)y and f: = e" z z + y? If, f = = frâ + fyŷ…

A: a) Given f=fx+fy+fz and F→=fx x^+fy y^+fz z^ and  fx=4xz2, fy=yz, fz=xz So, we have f=fx+fy+fz…

Q: 7. Find the rectangular equation if r = 4 cos 0 + 4 sin 0 (a) (c) x² + y² = 4 x² + y² = 4(x + y) (b)…

A:

Q: (c) y/" + 4y = 3r cos(2r)

A:

Q: y" + 4y – 5y = –260 sin(5x).

A: To solve the given differential equation

Q: d dr -x² + e³¹ - tan(x) dy²-sin(y) dy cos(y) +2 d dx -√x+e²

A:

Q: cos(t)y'-tsin(t) = y ; is this seperable or non-seperable?

A: It can be shows that it is not separable. See the next step