Use differential to approximate the change in the volume of a sphere when its radius changes from 2 to 2.1. The volume of a sphere of radius r is 4/3pir^3

Q: Find the area bounded by the curve x = (y+1)2 and y+1 = x2. Show complete solution of points of…

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Q: What is the volume of a rotational body formed by rotating the area bounded the = 4-x ² function…

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Q: Use differential to approximate the change in the volume of a sphere when its radius changes from 2…

A: Use differentials to approximate the change in the volume of a sphere when the radius is increased…

Q: Estimate (2x – 5) dx using right endpoints for n = 3 approximating rectangles. (2x – 5) dx is…

A: We have to estimate the , ∫15(2x-5)dx using right end points for n=3

Q: Compute the surface area of revolution of y=sinx about the x-axis over the interval [0,3π]. Surface…

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Q: With y > x > 0, find the area of the region between the y: curve, x = 0 and x = y lines %3D with a…

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Q: Use the Trapezoidal Rule to estimate the integral |dx using n = 4. What n is needed for 2 decimals…

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Q: Evaluate the volume of the surface of the shaped recreated by revolving the line y = 1/x as x goes…

A: Solution is written in below steps.

Q: How to compute for the differential volume of each coordinate system and its phase area?

A: Hints: We have to discuss that how to compute for the differential volume of each coordinate system…

Q: Find the area bounded by the curve y = 1+x² and the lines y = 0, x = y and x = 2. Show complete…

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Q: O Use differentials to approximate the increase in the area of a soap bubble when its volume…

A: Given query is to find approximate are increased.

Q: The possible error involved in measuring each dimension of a right circular cone is + inch. The…

A: The propagated error dV = V'(r)dr, here dr = +0.1 or -0.1 inch and r = 4 inches.

Q: Write the integral that gives the surface area generated when the curve is revolved about the…

A: Solution: The objective is to write the integral that gives the surface area generated when the…

Q: Find the volume of a right circular cone with height 18 and base radius 9 using integration.

A: Take a cross-section area of thickness dx at a distance x from top, integrate it from 0 to 18.

Q: Find the approximate surface area of a sphere of radius 3.02 in. (Use differentials)

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Q: Use the linear approximation to estimate the percentage change in volume of a right circular cone of…

A: Let V,  r  &  h be the volume, radius and height of the right circular cone respectively. Given,…

Q: FIND THE CENTROID OF THE REGION IN THE FIRST QUADRANT BOUNDED BY THE GRAPH OF y=9-x2, THE X-AXIS,…

A: Given region is bounded by the graph of  y=9-x2, The X-axis and Y-axis

Q: Find the area of the surface formed by revolving the graph y=x on the interval [0,3] about x-axis.

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Q: Use differentials to determine the approximate area, dA, of a circular ring which has an inside…

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Q: Find the area of the loop of the curve y2=x3 (1-x)6. Show complete solution of points of…

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Q: The area under the curve is negative, if z value is also negative. True or False?

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Q: valuate the integral

A: Given: ∫sin4tcos4t dt

Q: The diameter of a spherical ball bearing was measured to be 7.8 mm with a possible error of 0.07 mm.…

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Q: Find the area of the surface generated by revolving the curve about the indicated axis.   y = x 2/4…

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Q: Find the volume generated by revolving the area bounded by the curve y = (1 − x2)2 and the x-axis…

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Q: Evaluate the definite integral that represents the area of the surface generated by revolving the…

A: to find:- surface area of revolution about x axis.

Q: The thickness of the shell is a = 0.7 centimeter. Use differentials to approximate the volume of the…

A: Volume of sphere V= 43π×r3 From given figure radius is 100 cm .

Q: I'm stuck on this question and I don't know how I should be approaching this. What should I do?

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Q: Use differential to calculate the volume of the material needed in making a thin sphere with inner…

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Q: Find the area in the first quadrant bounded by the curve Y = 4–?^2 and the axes using horizontal…

A: Consider the region bounded by the the curve and the axes in the first quadrant

Q: The area bounded by the curve y^2 = 12x and the line x = 3 is revolved about the line x =3. What is…

A: Recall: Formula for volume,    V=π∫ab(radius)2dy Given,  y2=12x Substitute x=3 in the above…

Q: Sketch the region whose area is given by the definite integral. хр y3 Use a geometric formula to…

A: Given query is to find the value of the integral

Q: Find the most general antiderivative or indefinite integral. Use a capital letter C to denote an…

A: ∫ dx/(1-x2)sin-x lets substitute u = sin-x du/dx =1/(1-x2) du = dx/(1-x2)  ∫ du/u = lnu + C put u =…

Q: The closed right circular cylindrical can of smallest surface area whose volume is 686r cm³ has a…

A: Topic = Mensuration

Q: Calculate the area of the yellow and red curves using definite integral.

A: Consider the equation

Q: Assume a pink paint spill spreads in a circular pattern whose radius increases at a rate of 2 in/s.…

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Q: Find the volume generated by revolving about the line x=0 the area under the arch of the sine curvey…

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Q: Find the volume of the solid formed by rotating the region enclosed by y=e2x+1, y=0, x=0…

A: Given that: y=e2x+1,  y=0  ,  x=0  ,   x=0.5

Q: (b) Use differentials to estimate the maximum error in the calculated volume. What is the relative…

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Q: The Trapezoidal rule is a numerical method that approximates the value of a a. definite integral b.…

A: The trapezoidal  rule is a numerical method that approximates the  value of a

Q: Use integration by parts to evaluate the indefinite integral: 6ze dr

A: Use integration by parts method

Q: Determine the volume generated when the area bounded by the curves y-sinx and y%3cosx from x-0 to…

A: Aim: We need to find the volume of the solid obtained by revolving the bounded region (light yellow)…

Q: Solve using iterated integrals. (with graph) Find the smaller area cut from the circle x2 +y2 = 25…

A: The objective is to find the smaller area cut from the circle x2 +y2 = 25 and x=3.

Q: The radius of a circular disk is given as 20 cm with a maximum error in measurement of 0.4 cm. Use…

A: Given: The radius of a circular disk is 20 cm ie., r = 20 cm  error in measurement is 0.4 cm ie., dr…

Q: Determine the volume generated when the area bounded by the curves y-sinx and y=cosx from x=0 to…

A: Solution :-

Q: Find the area of the surface formed by revolving the graph of y = 2Vx on the interval [0, 14] about…

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Q: What is the differential form for the total surface area of a frustum of a cone with l as the slant…

A: The curved surface area of a frustum of a cone is:

Q: 2. Determine the approximate volume of a cube whose edge is 19.95 cm, using differential. 3. Use…

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Q: The radius of a circular disk is given as 28 cm with a maximum error in measurement of 0.2 cm. Use…

A: Write the expression for the area of the circle and take the derivative.