Find the function with the given derivative whose graph passes through the point P. r'(0)=2+ sec ² 0, P(1.0) The function is r(0) = (Type an exact answer, using as needed.)

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A: NOTE: Refresh your page if you can't see any equations. . the given function is  substitute x=0

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A: Answer is Vertex is maximum point

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Q: Write the differential dw in terms of the differentials of the independent variables 7x+y u+z…

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Q: x² + y² + z ² = 4 => Z = √√√4-X²2²_- y² 器 23²³² = √4-x²-x2² , -Y 1 然 ³4 "√4-x²-y² ay x² + y²2y =…

A: Note:- you are have non calrityvabkur symmetry kgmf function. By clearing it i have solved it.

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Q: The value of the following limit is -1 Undefined +∞o None 1 0 -8 limn →→+∞ en+1 Senti dx x ln x

A: According to question,Given Limit,limn→+∞ ∫enen+1dxx ln x

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Q: 1 1 Calculate the gradient of h(x, y, z)=33 Vh= ← 1

A: calculate the gradient of h(x,y,z)=1x2.1y3.1z3

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Q: 3. Use cylindrical coordinates to evaluate 3 √9-x² [² [³²*² [√²²+³ (2² + y²) ³¹ dzdydz 0 Jo

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Q: 1. Solve the initial value problem y' -1 -2 1 4 2 5 2 -2 0 y, y (0) E 5 -1

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Q: Given fo²F0₂ f(x) dx = 6 and (a) [ f(x) dx $fº Fx (b) [³ 16 (c) [f(x) dx (d) 3 f(x) dx -5f(x) dx…

A: Given ∫03fx dx=6, and, ∫36fx dx=-1, to evaluate the following.a ∫06fx dxb ∫63fx dxc ∫33fx dxd…

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A: Given; f(x)=11lnx+6 on[1,6]

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Q: Given z = = f(x,y), x= x(u, v), values given in the table below. Zu(3, 3) = 15+dq y = y(u, v), with…

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Q: 6. Set up and evaluate a triple integral in cylindrical coordinates that will yield the volume of…

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Q: Find the work done by F(x, y) = 3yî + 2xĵ in moving a particle along x = 2y2 from (2, 1) to (8, 2).

A: The solution to find work done by given force is as follow.

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Q: 5. Find the least and greatest distances from the origin to a point on the circle (x - 1)² + (y −…

A: We know that circle equation is - (x-h)2 +(y-k)2 = r2. Here (h,k) is centre of the circle and r is…