Consider the following initial value problem: x" – 2x' – 24x = sin(7t), x(0) = 5, x'(0) = -1. Using X for the Laplace transform of x(t), i.e., X = L{r(t)}, find the equation you get by taking the Laplace transform of the differential equation and solve for X(s) help (formulas)

Q: (8) Find the differential for the function using logarithmic differentiation. y = (sin x) (sec); (A)…

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Q: 3 (8) Consider the curve given by 23 + x?y+ y³ = 1 Use implicit differentiation to find the equation…

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Q: f(x) = 3cos(x) - 4sin(x) f(x) = sec2(x) + pi cos(x) find the most general antiderivatives of the…

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Q: (i) (k) dx (tan x) dx (secx) = = (j) (cscx) = dx (1) :(cotx) = =

A: As per your request, we answer only parts (j) , (k) and (l).find using derivative rules

Q: 1 Find the derivative of g(x)= (x)sec(x) + a+ x* + cos - sin(x)

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Q: C. h(x) = 2x² sin(x) - x sin(x) – 15 sin(x); ONLY product rule, NO power rule.

A: Given; h(x) = 2x2sin(x) - xsin(x) - 15 sin(x)

Q: Find the derivative of this complex equation using logarithmic differentiation?

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Q: Find the derivative of the function. G'(x) = G(x)=√1-169x² arccos(13x) -168x V1-169x arccos (13x) -…

A: We need to find out the derivative of the function.

Q: A. If g(x) = x² sin(r)dt. find g'(x). Use the fundamental theorem of calculus. B. Find the equation…

A: (a) GIVEN: g(x)=∫0xx2sin(t2)dt From fundamental theoram of calculous, g'(x)=d(x)dx×(x2sin t2)…

Q: Use the rules to get a formula for the derivative of m(t) = In(t? + 3) vt? + 3 with respect to t Use…

A: Here we will apply basic rules of derivatives and chain rule of differentiation.

Q: The average rate of change of f(x) = cos(x) with respect to x as a changes from 0 to π is 2 OOO 2 -2…

A: We have to find the average rate of change.

Q: Find the derivative of the function. f(0) = cos(0²) f'(0) = =

A: Given   f(thita) = Cos(thita2)

Q: What is the purpose of implicit differentiation? To find dy/dx without having to solve for y To find…

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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.