Q1): Use total differential to find the percentage error in calculating the area that cut from a circle (shown in figure below) if an error of ±2% is made in measuring r and 0. r2 hint A = :

Q: The edge of a cube was found to be 20 cm with a possible error in measurement of 0.2 cm. Use…

A: As we know that; The expression for the volume of the cube is: V=a3    ....(1) Where a is the edge…

Q: Use Simpson's rule with interval h = 1 to determine the approximate value of 6 V(1 + x³)dx. Give…

A:

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: he measurements of the base and altitude of a triangle are found to be 38 and 42 centimeters,…

A: The solution is :

Q: Find the total differential, given: (b) \theta = arctan (y/x)

A: Let us consider the function z=f(x,y)  The partials derivative are obtained as…

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: 1) The length of the edge of a cube was measured to be 30 cm with a possible error in mea- surement…

A: Given:- The length of the edge of a cube was measured to be 30 cm with a possible error in mea…

Q: A company manufactures spherical ball bearings of radius 3 cm. The customer requires a tolerance of…

A: Given data is : Radius r=3 cm Tolerance is no more than ±1% , therefore dr=±1%

Q: The radius of a spherical balloon is measured to be 9 inches, with a possible error of 0.03 inch.…

A: we know that  surface area of sphere =4pi r^2 where r is the radius of sphere  Given radius of…

Q: 3) a) Use Simpson's rule with n=4. b) Estimate the error in the approximation. -2x dx jedx to…

A: Given integral is ∫06e−2xdx. a We have to approximate the given integral by using Simpson rule.…

Q: This is a linear DE. If arranged to its form, what is the integrating factor? * xdy ニ

A:

Q: Use Simpson's rule with interval h = 1 to determine the approximate value of f V(1+ x3)dx. Give…

A: Given integral is ∫021+x3dx and h=1. We have to approximate the given integral by using Simpson's…

Q: Suppose a snowball remains spherical while it melts, with the radius r shrinking at 2 inch(es) per…

A: Suppose a snowball remains spherical while it melts, with the radius r shrinking at 2 inch(es) per…

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 edge of a cube was found to be 30 cm with a possible error in measurement of 0.l cm. Use…

A: Let the edge of the cube be x= 30cm And given error in measurement of edge dx= 0.1cm a) Volume of…

Q: The radius of a circular disk is given as 20 cm with a maximum error of 0.3 cm. (a) Use…

A:

Q: For a given triangle, side y is measured as 10 cm, the horizontal side x as 20 cm and the included…

A: Concept: Estimating error using differentials: ∂A=∂A∂a∂a+∂A∂b∂b+∂A∂θ∂θ Here A is the area of the…

Q: The radius of a circular disk is given as 20 cm with a maximum error of 0.3 cm. a) Use differentials…

A: GIVEN The radius of a circular disk is given as 20 cm with a maximum error of 0.3 cm we need to find…

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

A:

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

A: Relative error

Q: Suppose the side length of a cube is measured to be 5 cm with an accuracy of 0.1 cm. a. Use…

A: The measurement of the side length is accurate to within 0.1 cm. Therefore,  -0.1≤dx≤0.1  The volume…

Q: A cylindrical tank has a radius of 8ft and a height of 10ft. Both dimensions are measured with a…

A: Given : Cylindrical tank has radius of 8 ft and a height of 10 ft,both dimensions are measured with…

Q: Suppose the side length of a cube is measured to be 5 cm with an accuracy of 0.1 cm. Use…

A:

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

A: Let's find.

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: The volume V of a right circular cone of radius r and height h is given by V = ⅓ πr²h. Suppose that…

A: Solution:Given         V=13πr2hFormula:(uv)'=uv'+vu'To compare the change in volume of the cone with…

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

A: Solution.

Q: The radius of a sphere is measured as 9 centimeters, with a possible error of 0.025 centimeter. (a)…

A:

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: 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 Simpson's rule with interval h = 1 to determine the approximate value of V(1 + x³ )dx. Give…

A:

Q: The radius of a circular manhole cover is estimated to be 16 in. with a maximum error in measurement…

A: Due to our guidelines I am solving only first problem  The radius of circular manhole r = 16 in

Q: While measuring the side of a cube, the percentage error incurred was 3%. Using differentials,…

A:

Q: The radius of a circular disk is given as 24 cm with a maximum error in measurement of 0.2 cm. (a)…

A: Solution:

Q: For the volume or a cylinder V = RR*H Find the total differential dV

A:

Q: 2) By compating aderivatives, find the Tay ior for tixl= la x at

A: By using Taylor series expension of lnx

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: Suppose a metal rod has length 20 cm and diameter 6 cm. If it is to be insulated, except for the…

A: Given: length,h=20 cmd=6 cmdr=0.001dV=?

Q: 6. The radius of a sphere is measured to be 7 cm, with a possible error of + (1/10) cm. Estimate the…

A: Volume of sphere   V=3π​r3/4 Percentage error in volume    ΔV​×100/V=3×Δr​×100/r =3*1*100/10*7= 4.3…

Q: 1. The edge of a cube was found to be 32 cm with a possible error in measurement of 0.1 cm. Use…

A: Given : Measurement of edge of cube a = 32 cm Possible error in measurement of edge is da = 0.1 cm…

Q: Suppose the side length of a cube is measured to be 5cm with an accuracy of 0.1cm. a) use…

A:

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

A: Topic = Derivative

Q: The measurement of the side of a square floor tile is 10 inches, with a possible error of 1/32 inch.…

A:

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

A:

Q: The radius of a spherical ballon is measured to be 10 inches, with a possible error of 0.04 inch.Use…

A:

Q: The edge of a cube was found to be 15 cm with a possible error in measurement of 0.2 cm. Use…

A: The given data is: Edge of the cube x=15 cmPossible error dx=0.2 cm

Q: If a current I passes through a resistor with resistance R ,Ohm’s Law states that the voltage drop…

A: Given the ohm's law relationship that is V=IR , where V is the voltage , R is the resistance and  I…

Q: Determine the mean and the rms values of the following by direct integration method a. f(t) = sint…

A: