Let y be a function such that y(1) = -9/4 , where Y(s) = L {y (t)}. If it is known that: (d/ds)[Y(s) · s]=1/s3 determine y(3.0).

Q: 324y/" – 180y' + 25y = 0, %3D y(0) = 8, y'(0) = 5. y =

A:

Q: Find the derivative

A: The first derivative of f(x) is represented byf'(x) and the second derivative is represented by…

Q: Consider the function f(x) = (x² – 6)(a² – 6æ) Compute the derivative. f'(x) =

A: In this we are going to use product rule of derivative to find out the solution so I'm providing…

Q: The function f(x) = 1 + x decreases to 1 as x- 0. Does f(x) dx exist?

A: Given function is f(x)=1+x-1f(x)=1+1x Given integral is evaluated as follows.…

Q: Compute for y = [x² + 2] y = 3 1 x2 dy dx x³ + 2x + 1 (x - 1)² 3 X

A: Given that a function  and we find derivative of this function with respect to x. Here we use…

Q: Consider the following function. H(x, y) = In(8x² + 3y²) (a) Find fxx(2,3). (b) Find fyy(2,3). (c)…

A:

Q: Recent studies seem to indicate the population of North America porcupine (Erethizon dorsatum)…

A: For the solution follow the next step.

Q: Find the derivative of the function. f(t) = (7t² - 4t + 1)3/2 21t – 6 f 't) = 7? – 41+ 1)² (72 – 4t…

A:

Q: (a) f(x) = Vx(x² + x – 4)

A: the given function is: f(x)=x3x2+x-4

Q: 2x Find F'(x) given F(x) = S t2dt. -2x

A:

Q: Find f(x) dx for each graph of y = f(x). (b) у (a) y 1

A: Integral of the function between the limits represent the area under the function. Since both, the…

Q: Find y as a function of t if 25y"- 70y' + 53y = 0, and y(5) = 8, y'(5) = 1. %3D y = %3D

A: Given: 25y''-70y'+53y=0  with the IVP y(5)=8 ,    and   y'(5)=1By…

Q: (d) Let h(x) g(f(x)). Use the figure below to find h'(1) or state why the derivative does not exist.…

A:

Q: Find the derivative of the inverse of f for t = 0,

A: The derivative of a definite integral is given by the second fundamental theorem of calculus as…

Q: Let f(x) = 6x2 + 7x - 5. Then the average rate of change of f(x) from 0 to 18 is the same.as the…

A:

Q: 49y" — 42y + 5y = 0, and - y(4) = 4, y'(4) = 1. y =

A: 49y''-42y'+5y=0, y(4)=4, y'(4)=1 Auxiliary equation 49m2-42m+5=0

Q: Determine whether the following functions are even, odd or neither. (a) f(t)=r² +cost 3t (b) f(t) =…

A:

Q: Find the derivative: y = (4 – x)(x³ – 2)

A: Given y=4-xx3-2

Q: For the function y = f(x)- T 2. I- + 3, a 2 0.5, find df-1 (f-')'(4) = Preview

A:

Q: Differentiate the function. h(t) = √√t - 7et -6 (F) h'(t) = -7e² =-- (1) t

A: The given function is: ht=t7-7et   As we know that; The Sum/Difference Rule: f±g'=f'±g' The Power…

Q: Differentiate the functions: 1. y = 3x – Vx 2. y = 2 – 3x – 3. Given the function f(x) = x³ – 5x +…

A: