Use the method of variation of parameters to solve the initial value problem x' = Ax + f(t), x(a)=x₂ using the following values. 1-e-+6e41 6e-t-6e4t A = x(t) = 5-6 1-2 f(t)= 40 60 ,x(0) = 0 -e¹+46e¹-e4t ***

Q: -5x2 – 3 If f(x) = then f'(0) is 4х + 2 O - 3 О 13 O - 1/3 Оз

A: Solving the problem by obtaining the derivative.

Q: Q3. Solve in terms of Bessel's function, the ODE x²y" + xy' + ((lnx)² + ¹) y = 0 1²)y=0_z=lnx.

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Q: Find an antiderivative F(x) of the function f(x) = - 2x²5x + 2 such that F(0) = - 15. F(x) = Now,…

A: On solving this we will get

Q: 1. h(x) = 5f(x) – 4g(x) Answer. h'(-2) =

A: Dear student as per our rule in one session we can only solve one question. Please post the other…

Q: If h(x)=√ 7 + 6f(x), where f(1)= 7 and f (1)= 2, find h(1). h'(1) = x

A: Given function Where

Q: r(x) = [(3x-2)/(2x)], find r '(x) O O [(3)(2x)-(3x-2)(2)]/2 O [(3)(2x)-(3x-2)(2)] / x²…

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Q: f(x)= 3x2 -2, find f '(-2) O -12 none of these answers O 12 6x

A: Consider the function  f(x)=3x2−2

Q: If f(x)-3x+3x and f'(0)-3( by using 2-points formula with h=0.5), then the value of a is Select one:…

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Q: If fix) = 4x and g(x) = x + 9, find (f o g) 'x) and g" '(1 'x). (fo g)" 'x) =D

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Q: If f(x) = 18x2 + 96 3 ³√√x' find f'(8).

A: Given Function:- fx=18x23+96x3

Q: Given f(4) = 13, f '(4) = 19, g(4) = 7, and g'(4) = – 10, find the value of h'(4) based on the…

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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: Suppose we have 3 motors that need to be operated for (x) number of hours the present worth is…

A: Point of intersection of two straight line is the point at which the , and coordinate of both the…

Q: Find fif f'(x) = 8x³ + 16x + 6 and ƒ(1) = −3. Answer: f(x) =

A: f'(x)=8x3+16x+6f(1)=-3∫xndx=xn+1n+1+c

Q: Sketch the graph of y = f(x) with emphasis on concavity. Label all the intercept points, relative…

A: Substitute some random values of x and obtain the values of fx. x fx -5 -2.08 -2 0 -1 0.25…

Q: Find the GS of 2 (x - α)² = where a is an arbitrary constant and you may want to consider "pilot" y₁…

A: As per the question we are given the following nonlinear first order differential equation…

Q: Find the value of the constants a and b given that F'(x)= 2ax + b, F(3)= 47, F(-2)= -3, and F(1)=3.

A: We have given F'x=2ax+b Then, integral on bothe sides we get ∫F'xdx=∫2ax+bdx Fx=ax2+bx+c where c is…

Q: 5. Given: f (x) = ax³ – 9x² + 2x – 4 and g(x) = bx³ – 5x² + 62x + 70 | Solve for all values of a and…

A: We have to find

Q: 3x-5 12x+41 7. The derivative of g(x) = 8. The derivative of y = V5x² – 6 is y' = is g'(x) = (4x+7)2…

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Q: Find g' (6) given that f(6) = - 3 and f' (6) = 6. Enter the exact answers. (a) g(x) = 7x² – 6f (x)…

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Q: If x = e*-Y then is equal to A) B) log z (1+log z)* C)

A: solution:-xy=ex-ytake log both sideslnxy=lnex-yylnx=x-ydifferentiate both sides w.r.t…

Q: If f(x) = V5x – 3, find f-1(x). 3 3 f-(x) = 5x- x3 C. A. f-1(x) 3 x3 f-'(x) = 5 5 D. C. f-1(x) = 53…

A: To find the inverse of the given function f(x).

Q: '(x) = 7ex − 8x; f(0) = 16

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Q: 17. Solve the equation x-3x' + 3x +x-6 0

A: We have to find the solution

Q: Consider the function f(t) = 4 sec²(t) — 8t². Let F(t) be the antiderivative of f(t) with F(0) = 0.…

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: Given f''(x) = 9x + 5 and f'(-3)=-3 and f(-3) = 6. Find f'(x) = and find f(2)

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Q: C is the curve y = e® from (2, e²) to (0,1) and F = (x², -y), compute ſ, F-dr.

A: Given that, C is the curve y=ex from 2,e2 to 0,1 and F=x2,-y Then, F=x2,-y=x2,-ex So, F→=x2i^-exj^

Q: h(x) = px³ + 4px + 1, where p and q are constants. Given that h(-1)=-41 and h'(-1)=67, find the…

A: h( x ) = px3 + 4px + qxh( -1 ) = -41 h'( -1 ) = 67

Q: If f(x) = f'(x) = f'(1) = 6x + 2 7x + 2 find: 2 (7x + 2)² 28 (7x+2)³ X

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Q: If f(x) = 5x4 – 2x3 –x² + 3x – 1, then | f'(0) = d2 ;f(0) = dx f"'(x)= d4 ¡f(x)= dx

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