solutions of the above eqation is given by y1(x) = sinh(2x).  The solution of th

Q: Find g(x) if g (x) = (30x² – 60x) - 75»²–15z² and g(0) = -3. Round any numbers to 4 decimal places…

A: We use substitution method

Q: Suppose = f(). (a) Given y(xo) = yo, when does this equation have a unique solution? (b) Make a…

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

A: Given Differential Equation

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: Suppose f(x) is a differentiable function with f(-1) =2 and f(2) =-1. The differentiable function…

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Q: 33 + 5f(x)+7²(f(x))° = 0 and f(-2) = –1, find f'(-2).

A:

Q: Solve using the method of undetermined coefficients: y" + 3y" – 10y' = 2 + xe* %3D

A: Given: y''' + 3y'' - 10y' = 2 + xex

Q: In general, solving y' = 0 leads to Select an answer .2 Now, let y = f(x) 9 In(æ|). Determine y'. 2…

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Q: Given f(x)=-25sin (Sx) and f₁0) = -5 and f(0) = 4 Find F(1) 2

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Q: Let f(x) be a quadratic function such that f(0) = −2 and √ x²(x + 5/6 dx is a rational function.…

A: We are given that f(x) is a quadratic function that satisfies the condition f(0) = -2.Also, is a…

Q: If 1 1. f(x)dx = n(x) - tan(x) - 4² + x² + 6x + 0 4e C 3 then find f(x)

A: We can find f(x) as below, by finding the derivative.

Q: g(x)=√(x² - 1)², find g'(x) O none of these answers O (2/3) (x²-1)-1/3.2x O (2/3) (x²-1)-1/3 O (2/3)…

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Q: If 6√√x + 15√y = 177, find y'(x) by implicit differentiation. y'(x) = Y I Find the exact value for…

A: Given :The function is shown as To aim : The aim is to evaluate the function by derivative with…

Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (-) < 0, ƒ (x) has a root in [0, 1]. To…

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Q: Suppose that you are asked to find the point on the curve y=ln(x) such that the tangent line passes…

A: Given, the curve                              y =log(x) such that the tangent line passes through…

Q: uestion hat is y' (x) when y(x) = (4x³ + 6x)*?

A: * Logarithmic function property : ln ( an ) = n ln ( a ) * Product rule of derivative : ( f • g )…

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

A:

Q: f"(x) = f(x) = (x + 6)(x − 6)(x +,5)(x – 5) X Solve the equation f'(x) = 0. (Enter your answers as a…

A: To find second derivative of

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: For each of h(x) find h'(x): (a) h1(x) = . Hint: Use Quotient Rule.

A: Proceed as shown below

Q: Find the general antiderivative of each function. (can check by taking the derivative) F(X)= 12x3…

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Q: Find the second derivatives, f"(x) of O a) b) f(x) = 2x² + e²² F"(x) = 2e² (4x²+4) F"(x) = 4+e²²(x²…

A: dxndx=nxn-1dexdx=exd dx(a.b)=a.dbdx+b.dadxf(x)=2x2+ex2

Q: Consider the following functions. (x) = 2 + x, f,(x) = x, f;x) = x² g(x) = c,f,(x) + cof2(x) +…

A: A set of vectors {v1,v2,...,vk } is linearly independent if the vector equation x1v1+x2v2+···+xkvk…

Q: 2. Let X"(t) =| X®(1)=| be solutions of X'(t)= P(t)X, t>0 (a) Find W(X"(t), X®)) (b)Find P(t). (c)…

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Q: The tangent line to g(x)at x=3 is L(x)=7x−26 (see the diagram below). Find h′(3)where h(x)=(g(x))^4.…

A: Given h(x) =(g(x)) ^4 To find h'(3)