Use differentials to approximate the increase in the area of a soap bubble when its volume increases from 36 cm³ to 37 cm³.

Q: A coat of paint of thickness 0.02 cm is to be applied uniformly to the faces of a cube of edge 21…

A: We know that,

Q: Use differentials to estimate the value of 7+(1.02) correct to four decimal places.

A:

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: Use the differential dV to estimate the change in volume of a sphere when the radius changes from 9…

A: ddxxn=n xn-1

Q: Use linear approximation or differentials to estimate the following

A: Solution: Consider the given number: 1000.033 Let y = x3 = x13 Differentiating with respect to x:…

Q: The dimension of a box are b, b + 1, b + 4 . Find how fast the total surface area A increases as b…

A: Given that sides of box Length L=b Height h=b+1 Width w=b+4

Q: Use differential to approximate the change in y=x3+x2 as x changes from 1 to 0,95.

A:

Q: Use a linear approximation (or differentials) to estimate the given number. V 99.4

A:

Q: The edge of a cube was found to be 107 cm with a possible error in measurement of 0.03 cm. Use…

A:

Q: Use differentials to estimate the amount of paint needed to apply a coat of paint .05 cm thick to a…

A: Using differential to estimate the amount of paint needed to apply a coat of paint of 0.05cm thick

Q: (a) Use differentials to approximate the possible propagated error in computing the area of the…

A:

Q: Write the differential formula that estimates the given change in volume or surface. Then, use the…

A: Let y=f(x) be a differential function.  differential dx  is an independent variable.  the…

Q: Use a linear approximation (or differentials) to estimate the given number. 99.8 9.9

A:

Q: use differentials to approximate the change in y if x changes from 25 to 25.3

A:

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: Use differentials to approximate V36.1. 3.

A: Consider y = root x.Let take x = 36 and delta x = 0.1.Find delta y as follows.

Q: A spherical ball is measured to have a radius of 6 cm with a possible measurement error of ±0.1rmcm.…

A:

Q: Use differentials to estimate the amount of metal in a closed cylindrical can that is 30 cm high and…

A: Given a closed cylindrical can has height 30 cm and 6 cm is diameter. the metal in the top  and…

Q: 8. Use differentials to approximate the change in the volume of a cylinder if the height is…

A: Let's find.

Q: A coat of paint of thickness 0.04 cm is to be applied uniformly to the faces of a cube of edge 30…

A: Given that a coat of paint of thickness 0.04 cm is to be applied uniformly to the faces of a cube of…

Q: The diameter of a circular disk is measured as 30 cm with a maximum error in measurement of 0.2 cm.…

A: Given that :- Diameter = 30 cm , error = 0.2cm Area of circular disk = πr2 . Where ( r = d/2) So ,…

Q: The dimensions of a closed rectangular box are measured as 97 cm, 60 cm, and 30 cm, respectively,…

A: Let the dimensions of the box be l, w and h (for length, width and height).Surface area of the box…

Q: A spherical balloon is inflated with gas at the rateof 800 cubic centimeters per minute. (b) Explain…

A: To find the rate of change of the radius, differentiate the volume of the sphere, V=43πr2 with…

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: Use differentials to estimate the amount of paint needed (in m^3) to apply a coat of paint 0.04 cm…

A: Given that     A hemispherical dome with diameter 56m. Here we have to use the differentials to…

Q: a hemischperical dome has a diameter of 50 m. use differentials to estimate the amount of paint…

A: the problem concerns an application of differentials

Q: A cylindrical shell has a thickness of 0.2 cm. Using differentials, approximate the volume of the…

A: Solution.

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 thickness of the shell is a = 0.5 centimeter. Use differentials to approximate the volume of the…

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Q: Air is pumped into a spherical balloon at the constant rate of 200 cubic centimeters per second. How…

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Q: Use differentials to estimate the relative error in the lateral surface area of a right circular…

A: To find out the relative error in the lateral surface area of the cylinder.

Q: The edge of a cube was found to be 30 cm with a possible error in measurement of.1 cm. Use…

A: Consider the edge length of the cube is a , so the volume of the cube is: V=a3 The surface area of…

Q: write a differential formula that estimates the given change in volume or surface area. The change…

A: To write the differential formula that estimates the given change in volume or surface area.

Q: The dimensions of a closed rectangular box are measured as 88 cm, 53 cm, and 32 cm, respectively,…

A: Given: The dimensions of closed rectangular box is : =88cm×53cm×32cm

Q: Use differentials to approximate the value of (3.01)2 + 2(0.99) – 3 in four decimal places.

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Q: Find the total differential. z = ex tan(y)

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Q: The dimensions of a closed rectangular box are measured as 74 cm, 51 cm, and 50 cm, respectively,…

A: For a function y=fx, ∂y,∂x,dy and dx represents partial derivative of y and x and then differential…

Q: Find the total differential.

A: w=3x+y4z-9y

Q: The outside diameter of a thin spherical shell is 12 feet. If the shell is 0.3 inch thick, use…

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

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Q: Use differentials to estimate the amount of paint needed (in m³) to apply a coat of paint 0.07 cm…

A:

Q: A goldsmith is tasked to coat a closed rectangular box with gold 0.1 cm thick. The height of the box…

A:

Q: Use differentials to estimate the amount of paint needed to apply a coat of paint 0.03 cm thick to a…

A: The diameter of the hemispherical dome is 42m.The volume of the hemisphere is,

Q: Use differentials to estimate the relative error in the lateral surface area of a right circular…

A:

Q: Use the total differential approximation to calculate sqrt((3.91)(9.11))

A: Use the total differential approximation to calculate sqrt((3.91)(9.11))

Q: Use differentials to approximate the change in the BMI when weight increases from 55 to 56.5 kg and…

A: Let's find.

Q: The edge of a cube was found to be 30 cm with a possible error in measurement of 0.1 cm. Use…

A: (a).            Volume of cube :                       V  =  x3                      dV  =  3 x2…

Q: The thickness of the shell is a = 0.5 centimeter. Use differentials to approximate the volume of the…

A: Given:        a=0.5 cm       r=100cm     Volume of shell V=43πr3     differentiating on both sides…

Q: Use differentials to estimate the amount of tin in a closed tin can with diameter 6 cm and height 20…

A: Since volume is a function of both radius and height, therefore we will use method of partial…