The general solution for x' = + 3 1 a) x(t) = G e-21 + C₂ (₁¹) e b) x (1) = a (1¹) e (1¹) ₁²¹ + ₂(1) ₁ 0₁² -2t Te 21 te 5 c) x(t) = q e-2t 1 (1²)] + ₁₂ (₁²) 0² 1 d) x (1) = q (17¹) e ² + c ₂ (²) ² x(t)= (i)e²². 5 5 - x is:

Q: 2. Ifƒ (x, y) = log (x² + y²), then ƒ +ƒ is equal to XX yy 1 (a) x² + y² (b) 0 1,² - x² (c) (d) *…

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Q: Let h(x) = f(x)g(x). If f(x) = 4x² – 3x and g(x) = In(3x – 1), what is h' (x)? Select the correct…

A: The given functions are fx=4x2-3x and gx=ln3x-1. Here,  hx=4x2-3xln3x-1.

Q: Find the second derivative of the function f(x) = 2 – 3x + 5æ/2 – 7e" . 15 f"(x) = –3+ 2 7e" f" (x)…

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Q: then find f(x). | f(x)dx = = ln([x]) In(x) - sec(x) - 4e + 2 -x + 6x + C

A: The integration of f(x) equal to the;  ln(|x|)-sec(x)/3 -4ex/4+x2/2 +6x +C.

Q: 5) Given functions T(x) = 3x – x² and S(x) = 4x – 1 find the following: a) (T • S)(x) b) (T – 5)(-)…

A: Note:  In (T o S)(x) , s(x) is input. (T-S)(x) = T(x)-S(x).

Q: Given that g(2)=4 and g'(2)=3, what is the value of h'(2) for the function h(x) = In(g(x))? O 4/3 O…

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Q: If f (x) = – sin(x), then f (10) (x) is equal to A - sin(x) В - cos(x) C sin(x) D cos(x)

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Q: The general solution of the 1st-order ODE, (x + 3y - 2)y' = e=3(x+3y-2)² - y - 1/3(x - 2) is

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Q: If g(t) : 3t4 + 2t? – 7 find - g(0) g'(0) g''(0) : g'''(0) g(4) (0) (5) (0) ||

A: Given that, g(t)=3t4+2t2-7. Obtain the value of g(0). g(t)=3t4+2t2-7g(0)=3(0)+2(0)-7g(0)=-7 Obtain…

Q: Suppose f(-10) = -9 and f'(-10) = 8. Find the following. d (10x² + x − 9) ƒ(x) at x = − 10 is dx d…

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Q: (e) y(ª) – 4y "= 5x² -e2* (g) y(“) +8y '= 4

A: The given differential equation is y(4)-4y''=5x2-e2x

Q: Let y f(x) be the solution of the equation 49 dy sin I dr uch that f(n) = 1. What is the value of

A: Here the given differential equation is a linear differential equation, so to find the solution we…

Q: Given f(3)=0,g(3)=5,f'(3)=−7,g'(3)=−19 Answer the questions below: a) k(x)=4f(x)−3g(x) k'(3)=   b)…

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Q: Given f(2) = 3,f'(2) = 4, g(2) =-2, and g'(2) =-4. Find h(2) if h(x) = fx) × g(x). O-16 O 20 o 16…

A: Given that : h(x)=f(x).g(x) Now, taking the first order derivative, we get:…

Q: If g(t) = −3t¹ – 5t² – 6 find g(0) -6 g'(0) = 0 (0),,6 -10 g"" (0) g(4) (0) = g(5) (0) = = -72t

A: On doing differentiation  of given function we will get

Q: If the functions y₁ and y2 are linearly independent solutions of y" + p(x)y +q(x)y = 0, then its…

A: Given the functions y1 and y2 are linearly independent solutions of y '" + p ( x ) y' + q ( x ) y =…

Q: he Solve the (D+D+1)y(x) = xe equation er y,(x)= (x -1)e* - (x-1

A: Differential equation

Q: Oil flows into a tank according to the rate F(t)= and at the same time empties 1+t out at the rate…

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Q: nctions f(x) = 3 + VI, 9(x) = x² – 3, %3D (a) (fo g)(x) (b) (go m)(r)

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Q: Given that f(x) = x³ + e-2, and that g(x) = f-1(x), find g' (9). (Hint: f- (9) is a solution to the…

A: The function is fx=x3+ex-2 The function is gx=f-1x

Q: 5. y = gezt + cze-3t – cost o y" - 7y' +y = sint + cost o y" +y' – 6y = 5 sint – cost o y" +y' +y =…

A: Find y , y' and y'' and substitute in the given option and check which option is true. Note : As per…

Q: Let k(x) = (4x²)g(x)h(x). Given the following table of values, find k' (1). -1 1 1 0 1 -4 0 2 1 -1…

A: The given function is .To find the value of .Derivative formula:

Q: Assume f(7) = 0, f'(7) = 14, g(7) = 1, and g'(7) = . Find h'(7) given h(r) = g(x)

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Q: Find f(x) if f" (x) = 2, f(0) = 1 and f(1) = 0.

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Q: ) (a) Let f(x) = 6 + f'(x) and f'(4). f'(x) = ƒ'(4) = - x + C 6 Find

A: As per the guidelines  we are supposed to answer only one question at a time. If you want answers of…

Q: Evaluate: J-1)–1) dy 0-my-1-등u-1)" + 즐피 ++ 11-arctan(Y )+c arctan () +c V3(2y+1) O-m-- 1³ + }n² +…

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Q: Derivative. The derivative of h(x) : 3+ e(4x2 + 5) is O none of the other answers -e(4x + 5)…

A: step 2 complete solution

Q: 2. Use chain rule to find the derivative of the following functions (Hint: for function composed…

A: NOTE: Refresh your page if you can't see any equations. . Since you have asked multiple questions,…

Q: Solve y = (1 + y) sec (x) + tan (x) a. y = (x + c) [sec (x) + tan (x)] b. y = (c x) [sec (x) + tan…

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Q: 1.2y" - 5y' - 3y = 0

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Q: f 3, (n) =4 and Je (n) = 2 no lution of ny"- y'=0 ane -a why explain wa g.ln) +G ya (n) is also a…

A: The objective is  to prove the above question.

Q: If g(t) = 3t4 + 8t? – 9 find - g(0) = g'(0) = g'"(0) : g'''(0) = g(4) (0) = g(5) (0) =

A: Given function g(t)=-3t4+8t2-9.

Q: Consider the following IVP: x" - 4x' + 4x = 4e2t; x(0) = -1, x'(0) = -4 Find the general solution. A…

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Q: f(x) = 1 1+el/z

A: Topic:- function

Q: If f(x) = x + 2 and g(x) = x² – 9, find a formula for g(f(x)). O a) g(f(x)) — х + 2х — 9х — 18 - b)…

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Q: Transform all Elements of the equation (t) into the Basis B and check their validity in the the new…

A: As per the question, we are given a system of linear equations in the standard basis and asked to…