Using the Laplace transform solve the following initial value problem x" - 2x + x = t - sint, x = x (t), x' (0) = x(0) = 0.

Q: If false state why.

A: Given,

Q: Question 4. Find f/ (x). (a) f(x) = xsinx (b) f(x) = sech-1x²

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Q: T (8) If g(x) = sin(x) *cos(x) find g'(-).

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Q: The derivative of the function f(x) = 25 x3 -6 x2 +7x- 88 at X = 3 using a step size of 0.5 and…

A: on solving we get

Q: 4 Use implicit differentiation to solve for y' if r4y2 - x³y + 2xy³ = (Show your work)

A:

Q: Va - 2 find: Va + 2 If f(x) = f'(x) = f'(2) = %3D Submit Question

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Q: In this question, we are going to estimate the value of (6/5)^1/3 without a calculator, with the…

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Q: Suppose that f has an inverse, ƒ(2) = 5, and f'(2) = What is (f~')'(5)? %3D

A: (a) Given that f has an inverse, f(2)=5, and f'(2)=-34 As  f(2)=5 so, f-1(5)=2

Q: Find h' (t) if h(t) = h'(t)= [] 5 1/3 2 3/7

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Q: Let f(x)=√4x² + 4x + 6 f'(x) = f'(5) =

A: To find f'(x)

Q: 3 | (x + 7)10(5x − 1) (8x + 8)² Use logarithmic differentiation to find the derivative of f. Let…

A:

Q: Apply the method of Example 6 to f (x) = sin x to determine f ' ( π/4 ) accurately to four decimal…

A: Given function is fx=sinx. To determine f'π4. Solution: Function is fx=sinx. Differentiating the…

Q: Find the derivative of (a) (교2 + 1)" (6) In(cos²(e2")) 2x (c) sin-1 e-1 dt x +1 In a

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Q: 6) Consider the exponential function f (x) = ex* [C:4] a) Determine the n-th derivative of f(x). b)…

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Q: read the following headline about COVID-19 vaccinations: "The vaccination slow down is slowing…

A: Headline about COVID-19 vaccinations is given as- "The vaccination slow down is slowing down.'' Now…

Q: II. Find the first derivative of the following functions 1) S(x) = [√² + (x¹+4)*]* 10

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Q: %3D Apply the Chain Rule to find the tangent line to f(x) = 4v2x- 6e2-*at x = 2

A: We want to find the tangent of the given function at x=2 We know that slope of the tangent at a…

Q: 5. A function y = sin x is transformed into = -sin (3x) - 4. What is a possible transformation?

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Q: If fx)=5x-1, g(x)=1/x, and h(x)=g(fx)), then what is h'(0)?

A: Given that h(x)=g(f(x)) Using chain rule we get: h'(x)=g'(f(x))f'(x) We plug x=0 So,…

Q: If f(x) = 15 to dt then f'(x) =

A: Note:-Since you asked multiple questions according to our policy we can answer only first question…

Q: x) such that f"(x)=2r' +3x-4

A: Integration: f''(x)=2x3+3x2-4x+5; f0=2, f1=0 ∫xndx=xn+1n+1+c

Q: Find a root of f(x) = 6 Sin (x)e- x + 1 using Newton Raphson Method accurate to 5 decimal places.

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Q: Q3: find the derivative of In(x4+3x-1) a) f(x) = %3D x²+1 b) f(x) = 4x³ . log(x² + 2x) %3D c) f(x) =…

A: Use product rule of differentiation.

Q: 23. g(x) = √√√9 — x Answer g'(x) = 1 2√9-x 9 (-∞, 9], (-∞, 9)

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