Calculate the surface area of revolution of f(x) = 3√(x) + 2 about the y-axis in [2,8]. Graph.

Q: The parabola y = x2 + C is to be tangent to the line y = x. Find C.

A: To find the value of C.

Q: /s. 5. Show that 2x?dx = f 2x²dx + S, 2x²dx + f 2x²dx %3D

A:

Q: Find all points on the graph of x2y − 2x + 63y = 2 where the tangent line is horizontal. (Enter…

A: Differentiate the equation x2y-2x+63y=2 wrt x:  ddxx2y-ddx2x+ddx63y=ddx22xy+x2dydx-2+63dydx=0

Q: Create a 3-D plot of the function sin(/x² + y²) Vx² + y² for -8 <x5 8 and –8 < x < 8.

A: Note: Here, we are considering -8 ≤ x ≤ 8 and -8 ≤ y ≤ 8 rather than -8 ≤ x ≤ 8 and -8 ≤ x ≤ 8. We…

Q: Find the points on the line 3x – 4y – 1 = 0 which are at a distance of 5 units from the point (3,…

A: Solving the problem by finding the points.

Q: f the line tangent to the graph of y =x* – 2x + 1 at x =-1

A: Idea: find the slope of tangent line by differentiation at x=-1 .then find the point on the curve.…

Q: (2) Determine the intersection points of y=-x² +9 and y = 5. Then find the area bounded by this…

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Q: Find the area of the segment cut from the curve y=x (x-3) and the ordinates x=0 and x=5

A:

Q: ifferentiate the funtion y = 2 csc (1-3x)

A: Giveny=2cosec(1-3x)Aim: dydx

Q: 3. v+ 4)(v² + 8y)}v\y² + 8y – 1 dy y²+ 8y- 1 dy

A:

Q: Use a change of variables to find the area of the curved rectangle above the x-axis bounded by…

A: Given,Area bounded by:y24-1≤x≤4-y216 , y264-16≤x≤9-y236 , x≥0