1. Consider L{y(t)} = Y(s). By solving the equation ty"(t) + 2ty(t)=0 con y(0) = 0 you have to: A) Y(s) = C 82-2 B) Y(s) = 72 C) Y(s)=C-e-2/2 D) Y(s) = C.e/2 All of them with C an arbitrary constant.

Q: Show that the equation f(x) =x+3x-1%=Ø %3D has at least one solution,

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Q: f(x) dx = -4, f(x) dx = 6, g(x) dx = 8 - If g(x) dx b. c. 3f(x) dx d. dx x) - g(x)] dx g(x)] dx e.…

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Q: Given h(x) = (-x² – 2x – 2), find h' (0)-

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Q: Solve for y(x): [y(x)³¹(x) = e³(x) y(0) = i

A: Given Differential Equation

Q: i(t) = (A₂ + A₁t)e-at

A:

Q: If f f(x) dx = 6, f f(x) dx = 2, and f, g(x) = -5, find f₁[2f(x) — 4g(x)]dx.

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Q: 16. (D² + 3D)y = -18x; y = 0, Dy = 0 when x = 0

A: Given differnetial equation ( D2 + 3D )y = -18x

Q: Solve csc(x) – 2 = 0 on [0, 27]

A: Let's find.

Q: g(x)dx = (5x? +2)° +C

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Q: What is the value of y(10) for y(t) L'((e“+2e ll + 3e ")) ?

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Q: f(x) = e + x³ – 1 and g(x) = 2r2 – 1. %3D Find (g of-)(e). · O C

A: Please refer to the image below

Q: x - 2xy - 3y" : y(1)=; dx

A: The given equation is first order Bernoulli's ordinary differential equation. y'+p(x)y=q(x)yn The…

Q: 3. Given f(x) = -7x-8-4sin(8)- 3e-6x – 4n² then determine the defining equation of f(x).

A: To determine the defining equation of f(x) from f'(x), we integrate f'(x) with respect to x.

Q: Let h(x)=f(g(x)). If f(−4)=−3, f′(−4)=−1, g(1)=−4, and g′(1)=3, find h′(1).

A: The formula one have to use here is f(g(x))'=f'(g(x))* g'(x)

Q: The formula for the quadratic function y = f(x) such that: f(0) = -35, f(-1) = -36 and f(1) = -32 is

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Q: If √(x) + √(y) = 7 and y(36) = 1, find y′(36) y′(36) = ?

A: Taking derivative with respect to x,

Q: Solve: (x+y)dy-(x - y)dx=0 A. x² - 2xy-y²= B. x² + 2xy + y² =c C. x² + y² =c D. x² - 2xy + y² =

A: The given equation is(x+y)dy-(x-y)dx=0 To solve the differential equation.

Q: Find | [3f(x) – g(x)]dx : i if 6 f(x)dx 2 and g(x)dx = 30 %3D %3D

A: Given: I=∫163fx-gxdx And ∫16fxdx=2 ; ∫16gxdx=30 We know that; the sum rule: ∫fx±gxdx=∫fxdxdx±∫gxdx…

Q: snip

A: Given  f(x)=exg(x)=3x-2 a) To find (f∘g)(2) (f∘g)(x)=f[g(x)]             =f(3x-2)             =e3x-2…

Q: Lizzie came up with a divisibility test for a certain number : Break a positive integer  into…

A: Introduction: The divisibility is the base of number theory. There are different rules of…

Q: Let h(x)=f(g(x)). If g(3)=−4, g′(3)=5, f(−4)=−6, and f′(−4)=4, find h′(3). Do not include "h′(3)="…

A: We have to find derivative of h(x) at x=3 .Information is given below:

Q: dy (d) 3y(x2 – 1) + (x³ + 8y – 3x) dx 0 =

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Q: If h(x)=6ex−5, find h′(x).

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Q: a.) If     f(x) dx   = 4x9 − 8x6 + C, find f(x). f(x) =

A: Given: ∫fxdx=4x9-8x6+c                                          ..1 for finding fx, we differentiate…

Q: A volume is described as follows: 1. the base is the region bounded by y = 8-2² and y = 0 2. every…

A: The base is the region bounded by y=8−12x2 and y=0. Every cross section parallel to the x-axis is a…

Q: (c) Solve for each of the following. dx (i) Vĩ + Jỹ = 4 (ii) y = 2x2+1

A: We have to find the first derivative of given function.

Q: Find the given value. g(x) = 5x3(x2 − 5x + 4),    g'''(0) g'''(0) =

A: Use derivative to get the value of g^"'(0).

Q: f(x) = e−x,    n = 5

A: Given:          fx=e-x ,n=5 A Maclaurin series is given by fx=∑n=0∞fnan!xn Here fx≈Px=∑n=05fnan!xn…