2) Using the standard Laplace Transforms in Slide 4, evaluate: a. L{5t³+3 sin 4t} b. L{3et5e-³t} L{cos 5t sin 6t} d. L{sinh 6t+cosh 9t} e. Le³t+cos 6t - e³t cos 6t}

Q: (b) L-¹{12} 8²-68+12}

A:

Q: I understand that the derivative of cosx is -sinx, but I need to show the work using trig…

A: We have to find the derivative of cos(x) by using definition of derivative by limit.

Q: Where are the theta valuss for the horizontal and vertical tangent lines on [0,2pi) of r=1+cos theta

A:

Q: (sinhz)(coth’z+csch*r)dz

A: Integration is done.

Q: If g(r,s,t) = et sin(st), find dsdr2*

A: Given Data: Function: gr, s, t=ertsinst   The triple partial derivative can be rewritten as,…

Q: 1.) Find the derivatives of a.) y = 3e²x — 2lnx + arcsec x

A: the given equation is

Q: 3) Find the minimum and maximum values y = 2x5 +5x² on the interval [-2,2]

A:

Q: Given that Le"}= - s- a 1 and that e = cos ot +isin ot , deduce the Laplace transforms for cos ot…

A:

Q: 2. Find each of the following transforms: (a) L[x² sin ax];

A:

Q: 6) By implicit differentiation find a) xy + y² = 2 find d²y/ dx² %3D b) sin(x²y²)= x find dy/dx

A:

Q: Find all Second partial derivatives fcx.y)- Sin?Cmx+ny)

A: Given that, f(x, y) = sin2(mx + ny) we have to find second partial derivative with respect to x and…