Find an expression as a definite integral for the length of an ellipse x2/a2+y2/b2= 1 by using the parametrization x=a sinφ, y= b cosφ and letting
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Find an expression as a definite integral for the length of an ellipse x2/a2+y2/b2= 1 by using th...
Find an expression as a definite integral for the length of an ellipse x2/a2+y2/b2= 1 by using the parametrization x=a sinφ, y= b cosφ and letting you should get We were unable to transcribe this image1-k2sin2 od
A rectangle with sides parallel to the coordinate axes is inscribed inthe ellipsex2/a2 + y2/b2 = 1:Find the largest possible area for this rectangle.
Evaluate each integral using the definition of the definite integral with right endpoints and taking the limit. (Note: You need to write out the Riemann sum and use the summation formulas.) (a) 0 (x^2+2x-5) dx x+b-a/n= xi=a+Ix= (b) 1 x^3 dx x=b-a/n= xi=a+Ix= We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Find a formula for the area of the ellipse 2) -1 by slicing vertically. Sketch the ellipse, + b2 a clearly showing a representative vertical slice. Show your Riemann sum and definite integral Recall that this is an ellipse centered at the origin with major axis length of 2a and minor axis length of 2b Note: If a b, what do you notice about your formula? Find a formula for the area of the ellipse 2) -1 by slicing vertically....
Derive the moment generating function of y= a x1+b x2, where y~ N( a 1 + b2 , a2 12 +b222 + 2ab cov(x1, x2) ), not both a and b equal to zero. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Find the absolute min/max of on the domain f(,y) = x2 + y2 +r+y + 4 We were unable to transcribe this image
First use (20) in Section 6.4. y'' + 1 − 2a x y' + b2c2x2c − 2 + a2 − p2c2 x2 y = 0, p ≥ 0 (20) Express the general solution of the given differential equation in terms of Bessel functions. Then use (26) and (27) J1/2(x) = 2 πx sin(x) (26) J−1/2(x) = 2 πx cos(x) (27) to express the general solution in terms of elementary functions. (The definitions of various Bessel functions are given here.) y''...
1. (a) Find L4 and R4 for the integral 1 (x sin x/2) dx Show the setup and round the answer to threedecimal places. (b) Find M4 for the integral 1 (x sin x/2) dx . Show the setup and round the answer to four decimal places. Sketch the approximating rectangles on the graph. (c) Compare the estimates with the actual value 1 (x sin x/2) dx 10.243 . Which estimate is the most accurate? (d) Express the integral from...
1. a) Find using integration by parts. Does the improper integral converge? b) What can you say about the infinite series using the improper integral in the previous part? Estimate the partial sum S100 = . Find upper bound for R100 = and use the integral test. We were unable to transcribe this imagepinsinity In(x)}dz We were unable to transcribe this image100 In(n) 2 73 n=101
Let S be the region bounded by the graphs of , , and the vertical line . a. Find the area of S b. Suppose S is revolved around the line . Using the cylindrical shell method, find an integral expression equal to the volume of the solid that is created. c. Now suppose S is the base of a solid. For that solid, each cross section perpendicular to the x-axis is a rectangle with height 5 times the length...