x' + æ = 9+ 5(t – 2), x(0) = 0. Find the Laplace transform of the solution. X(s) = L {x(t)} help (formulas) Obtain the solution x(t). (t) help (formulas) Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 2. if 0

Q: Find the derivative (df/dx) 1- f(x) = cscx - 4√x + 7y−² 2-f(x)=x² cotx-x-2 3-f(x) = (secx + tanx)…

A: We have to find derivative of given function.

Q: Find y as a function of a if y(0) = 7, y'(0) = 4, y"(0) = 133. y(x) = y" - 8y" -y + 8y = 0,

A:

Q: (b) A poll commissioned by a politician estimates thatt days after he makes a statement denegrating…

A: Given: Percentage of constituency that supports a politician is: St=75t2-3t+25t2+3t+25 Derivative of…

Q: Find an equation for the line tangent to the graph of 2x f(x) %3D x + 4 at the point (2,…

A: The standard form of the tangent helps to find the required equation. The standard form of the…

Q: 2-22 Differentiate the function: f(x) = log10(√x ) ? Please show work along with the rule used for…

A: We have to differentiate the function f(x).

Q: Prob. 6 (a) i) Let f(x) = 2x² - 3. Find f'(-2) using only the limit definition of derivatives. (b)…

A:

Q: Find the derivative of the function. Ax) = 6x (9 - 8x)* O (- 12x) (9 - 8x)' (6x- 9) O (-181 )(9- 82)…

A:

Q: a) Differentiate the function Q(p) = -2√/p³ (e-P-PB). b) Hence or otherwise, determine Q'(1).

A: The given function .The aim is to find the derivative function  and find the value of .

Q: 1. 5 Let the function s(t)- 111 x² + 10x + 15 represent the motion of a toy car as it travels near a…

A: Note: Since, the student has mentioned a typing error in the function and want to replace the x's…

Q: If point P (4,-3) is on f(x) and if g(x-2) = -3f(1-x) -5 , then determine the point P' on g(x).

A:

Q: On which interval is the function f(x) = x2 - 2x - 8 decreasing? A [-2, 4] B (-∞, 4) C…

A: Given, f(x) = x2 - 2x - 8

Q: Sketch a graph of the function f(x) = 2 sin(z) %3D 6+ 5 4 3 -6 -5 -4 -3 -2 -1 -- 6 7 -9 -8 -7 2 3 5…

A: How to solve: make a graph of sin(x) and then transform it one by one:

Q: The function g(x) is obtained by shifting the graph of y=x2. (a) If g(3)=36, give a possible formula…

A: If the graph shifts horizontally, then the point (3 , 36) on the graph of g must correspond to a…

Q: Find the derivative of f(x) = x In(x) 1- In(x) O In(x) O1+ In(x) O In(x) /x

A:

Q: Evaluate L{t cosh 4t. 1 1 + (s – 1)’' (s+1)* А. В. (s-1)* (s+1)* 1 1 С. (s –4)° (s+4)' 3. D. (s-4)*…

A:

Q: The average daily height of a river can be modeled with a cyclic function. The minimum average daily…

A: Given that: Minimum average daily height = 16 meters after 5 days gives y(5) = 16 Maximum average…

Q: Find the linearization of the function at x = 1. * f (x) = 2x³ - 3x + 7 O y = 6 + 1(x - 3) O y = 6 +…

A: Given, fx=2x3-3x+7

Q: Use Müller's Method to determine all the roots of f(x) =x' – x – x-2 Choose x2=1.0, Xo=X2+dx2,…

A:

Q: The total profit (in dollars) from the sale of x cell phones is P(x) = 15x – x² – 70 for 0<x< 60.…

A: Solution is given below:

Q: 2. Find the first derivative of each function: a/y = x³e; b/y = log6 (2x² - 3x + 6); c/ y = e2x cos…

A:

Q: y" + 4y' = 0, y(0) = -4, y'(0) = 6, y"(0) = –8.

A:

Q: Compute the derivative of f(x) = (3x² – 1)1/4. %3D - O (6x – 1)!/4 a(322 – 1)5/4 O 3 2*(3x² – 1)-3,…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.