Consider the following initial-value problem. y' y = 2 cos(6t), y(0) = 0 Find L{f(t)} for f(t) = 2 cos(6t). (Write your answer as a function of s.) L(f(t)) = Use the Laplace transform to solve the given initial-value problem. y(t) =

Find f. f ‴(x) = cos(x),    f(0) = 4,    f ′(0) = 8,    f ″(0) = 3

The figure shows how a function f(x) and its linear approximation (i.e., its tangent line) change value when a changes from co to xo + dx. Suppose f(x)=x²-3x, xo = 3 and dx = 0.02. Your answers below need to be very precise, so use many decimal places. (a) Find the change Af = f(xo + dx)-f(xo). Af=0 (b) Find the estimate (i.e., the differential) df = f'(xo) dx. df = (c) Find the approximation error | Af-dfl. Error = f(xo+dx) f(ro) Af = f(ro+dr)-f(ro) TO dar (Click on graph to enlarge) y = f(x) Error= |Af-df xo+da Tangent df = f'(x)dx

Find r’(t) for the function provided in the photo

Find f if ƒ"(t) = 2et + 3 sin(t), f(0) = −10, ƒ(π) = −8.

The phase shift of the graph of f(t) = sin (4t - TT) is?

Draw the curve of the function