Use the method of variation of parameters to solve the initial value problem x'=Ax + f(t), x(a)=x using the following values. -1 cos (t) - sin (t) (7) sin (t) cos (t) A = 0 = 1 f(t) = 3 sec (t) 0 ,x(0)= At x(t) (Use parentheses to clearly denote the argument of each function.)

Q: If f(x)=2 sin x/1+cos x, then f′(x) =    f′(4) =

A: We have to find

Q: If f(x) = cos(2x) then find II f (t|4)

A: Given query is to find the Indicated derivative.

Q: An object moves along the x-axis with velocity given by v(t) cos(t) m/s || Suppose that the object's…

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Q: 3. Find f. (a) f"(x) = x + 12x² %3D

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Q: f(x) = cos(√x) + 2 The slope of the tangent line to the curve y = f(x) at the point where x = 4 is A…

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Q: c If f" (x) = 18 cos 3x and f' (0) = f(5) = 1, find f(x).

A: The solution of the problem is given in the next step.

Q: Given f"(x) =| 16 sin(4x) and Find f

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Q: y = V4x² + 5x

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Q: Q3\ find General solution of sin (xy). (ydx + xdy) = 0 %3D

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Q: Find f(t) given that f"(t)=sin(x) + cos(x) - 10, f'(0)=10, and f(0)=20.  Please show steps. Thanks.

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Q: Let g(z) = 6e²+ 9 cos z Determine the derivative of g. g'(z) = 6e²-9 sin(z) ✓ Determine the…

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Q: f(x) = 3x cos ƒ'(x). -1 (2x + 4) − √√/19 − 3x², find

A: Given: fx=3xcos-12x+4-19-3x2. To Find: f'x.

Q: If f(x) = 5x(sin x + cos x), find f'(x) = 5 sin(x) + 5 cos(x) + 5x cos(x) - 5x sin(x) To two decimal…

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Q: Determine the lowest positive real root of f(x) = 8 (Sin x) (e-*)–1 using the Secant method. Take…

A: Solution: Given that

Q: If f(x) = 2 sin æ + 9 cos a, then f'(x) = f'(4) =|

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Q: The function f(x) = a sin x + b cos x + c satisfies f"(x) = cos x – 2 sin x, f'(0) = f(0) = 2. Find…

A: a=2 b=-1 c=3

Q: The derivative F' (t) is graphed in the figure below. Given that F (0) = 12, calculate F(t) for t =…

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Q: (a) Use f(t) = a cos (b(t- c)) + d to model these conditions. (b) Evaluate f(1) and f(7). (a)…

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Q: Ql:- Find the domain of the following functions a) S(x) = sin"*(2 – 3x) b) f(x) = sec"*(x – 2)

A: we have to find domain

Q: Find approximate value of the derivative for f(wo)-6f(x1)+3f(x2)+2f(x3) fr(x2) = f(x) = 10 sin(20æ?)…

A: Introduction: Numerical differentiation is the technique of obtaining the numerical value of a…

Q: 2. Find the anti-derivative of a. f(x) = 2x¹ - 5√√x³7−2e* ++ 3 1 1+x²

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: -1 Find the derivative of the function: y=6 sin ¹¹ (x²). y'= y'= O y'= 12x y'= -X 2x 2 + X 12x 4 4 X…

A: Given y =6 sin-1 (x2 )

Q: 7. Find the second derivative given g(x) = sin x² A. 2 (cos x² - x sin x²) C. 2x cos x² 9 "(x) - 4 x…

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Q: Q2\Find T.E of the function f (x) = sin 2x when a =1?

A: Given that  f(x)=sin(2x) at a=1  To find the T.E

Q: 2) Find the derivative of the following function 1² +5 1² – 5 (a). f(x) = (b). f(x) = 2 tan '(x) –…

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Q: Consider the function f(x) = 4 sin(x) cos(x) + 6 csc(x). Evaluate its derivative at the point x =…

A: Product rule of derivative is used.

Q: 6. Find the derivative of the following (express answer in simplest form): 1+ sinx a. f(x) = In…

A: Topic = Derivative

Q: 1-Find the first derivative of the following function f( x) 5 cos (10x) + x' – 2x – 6x+ 10 For x=2…

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Q: f(x.y) = xtan(). =tan( ес

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Q: Find (f −1)'(a). f(x) = 4x3 + 5 sin x + 2 cos x,    a = 2   (f −1)'(a) =

A: Consider the function f(x) =4x3+5sinx+2cosx.Compute the derivative of the given function as follows

Q: A2) Find the derivative of the following functions 1² + 3 z² – 3 (a). f(x) : (b). f(x) = 2 tan (x) –…

A: As per bartleby guidelines, we are supposed to solve only first three subparts if multiple subparts…

Q: 3) Find the following derivatives: a. y = 2x b. f(x) = 4x³10x² + 7x-15 c. g(x) = 3x(x² - 4)5 d. y =…

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