3. Find the value of c guaranteed by the MVT for integrals for f(x) = cos(x), [-; 3'3 ] over this interval.

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A: f(x)=cos h-1(x)domain of the function is [1, ∞)for z=cos h-1x+yxz=cos h-11+yx1+yx ≥1yx≥0

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A: use average velocity formula for finding the value.

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A: The given function is;  f(x,y,z)=xyz x2+y2+z2=243.

Q: 3. Determination of integrating factors: 2y(x+ y+2)dx +(y² - x² -4x-1)dy = 0

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A: Given problem:-

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A: Explanation of the answer is as follows

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A: I have provided this answer with full description in step-2.

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Q: Consider a triangle ABC like the one below. Suppose that a=50, c=68, and A=26°. (The figure is not…

A: Consider a triangle ABC like the one below. Suppose that a=50, c=68, and A=26°.To solve the…

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Q: d.The exact differential d xdy – ydx e what is the d 1 e. In the differential equation 2xydx+ (y²…

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Q: (n!)2 (x-2)2 is equal to The radius of convergence of the series .... .... n=1 3" (2n)!

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Q: Use the indicated change of variables to evaluate the double integral. 8(x + y)e* - Y dA x= u + v) X…

A: x=12(u+v)y=12(u-v)u=x+y, v=x-y(x, y)=(0, 0): (u, v)=(0, 0)(x, y)=(1, 1): (u, v)=(2, 0)(x, y)=(-1,…

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Q: ft号+号 13 4. 4 2.

A: We can solve this as follows:

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A: The graph is shown below:

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Q: dz Use the chain rule to find when %3D and s=2 t=1· - ds z=3x+4y, x=s³r?, _y=s²

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A: The given integrand indicates the circle: x2+y2=r2, with a radius of r units. Limit of the integral…