By the even extension method applied to the function f (x) = e-2", where x > 0, the value of the integral / 00 cos(9w) dw = 4 + w2

Q: Find f. f"(x) = cos(x), f(0) = 3, f'(0) = 6, f"(0) = 4

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Q: (a) [ dx ? 元+1

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Q: Find tan-1 x2 -dx using integration by parts.

A: Integral by parts

Q: D?/if w= Cos (X+y)+Sin (X-y) Show that

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Q: Find f. f"(x) = cos(x), f(0) = 6, f'(0) = 4, f"(0) = 9 f(x) =

A: We can find the value of f(x) as below.

Q: Use forward and backward difference approximations of O(h), and a centered difference approximation…

A: Given function is, fx=sinx1+cos Then the forward Oh is,…

Q: Find f. f "(x) = 7 + cos(x), f(0) = -1, f(71/2) = 0 %3D %3D

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Q: Solve for ((1 integral 0) x3(2+2x4)5 dx) instead

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Q: find the general solution of  xdy/dx+4y=(sinx/x)*(sqrt of y)

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Q: Apply the method of Example 6 to f (x) = sin x to determine f ' ( π/4 ) accurately to four decimal…

A: Given function is fx=sinx. To determine f'π4. Solution: Function is fx=sinx. Differentiating the…

Q: Find f    if  f'(x) = 7x9 − 5 √x + 3 sin x,   f(0) = 4

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Q: Show that cosh (3x) = 4cosh³r - 3 cosh T.

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Q: sinx

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Q: Solve the DE by eliminating the arbitrary constant of x sin y + (x^2)y = C

A: Given that the expression xsiny+x2y=C. Differentiate with respect to x.…

Q: #4 tan lun sec x dx 4.

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Q: Find f. f"(x) = x³ + sinh(x), f(0) = 4, f(2) = 5.6

A: f'' ( x ) = x3 + sinh(x)   , f ( 0) = 4, f ( 2 ) = 5.6    To Find: f ( x )

Q: If f(x) = sin?x, then f"(x) = %3D A 2cos2x B cos2x -sin2x D -4sin2x

A: Given, f(x) = sin2x For the given function , applying chain rule ,  First differentiate it as { xn ,…

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: find the integration of 1/(sinx*√(sin(2x))) .dx

A: Let's find.

Q: J (sec²4x) (tan 4x)dx

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Q: Find a root of f(x) = 6 Sin (x)e- x + 1 using Newton Raphson Method accurate to 5 decimal places.

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Q: dy/dx+ytanx=cos^2(x)

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Q: Show that (a) L-1 = sin(at) - tcos(at) %3D (s²+a²)²) (where L indicates imverse Laplace transform)…

A: L-11s2+a22=12a2sin(at)-12a2tcos(at)

Q: Find f. f "(x) = 9 + cos x, f(0) = -1, f(7t/2) = 0 f(x) =

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Q: Find f. f '(t) = 2 cos t + sec?t, , -1/2 < t < «/2, _f(x/3) = 3 f(t) =

A: Given: The derivative function f'(t)=2cost+sec2t , -π2&lt;t&lt;π2 , fπ3=3. To find :  The function…

Q: Differentiate f (x) = (cos 3x)V* %3D

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Q: Evaluate the definite integral I^V₂ x² + 4x(x³ + 1) dx a) Find an anti-derivative •√√₂¹ +² b)…

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Q: Find f. f ''(x) = 3 + cos(x),    f(0) = −1,    f(7π/2) = 0

A: Given function: Now,