hw14S3.5 - hw14S3.5 4(08 PM JAE HYUN PARK Math 124 section...

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12/14/16, 4(08 PMhw14S3.5Page 1 of 17Current Score :104 / 104Due : Wednesday, November 2 2016 11:59 PM PDT1.18/18 points | Previous AnswersThe graph of the equation 2x2+ xy+ y2= 4 is the tilted ellipse pictured below; i.e. the points (x,y) inthe plane that satisfy the equation yield the pictured ellipse. This is NOT the graph of a function y=f(x). However, if you solve the original equation for yin terms ofx, you can break the graph into two pieces, each of which is the graph of a function as pictured below.(a) The upper piece of the ellipse (solid) is the graph of the function y=g(x)=$$x+167x22hw14S3.5 (Homework)JAE HYUN PARKMath 124, section D, Fall 2016Instructor: Dmitriy DrusvyatskiyWebAssignThe due date for this assignment is past.Your work can be viewed below, but no changes can be made.
12/14/16, 4(08 PMhw14S3.5Page 2 of 17(b) The lower piece (dashed) of the ellipse is the graph of the function y=h(x)=$$x−√167x22(c) There are two points indicated (as big dots) where the graphs of the functions in (a) and (b)"glue together". What is the x-coordinate of the right-most point?$$47(d) The implicit derivative is dy/dx=$$4xyx+2y. (e) Setting the denominator of (d) equal to zero yields the linear equation: y=$$12x (f)Simultaneously solving (e) with the original equation gives |x|=$$47
12/14/16, 4(08 PMhw14S3.5Page 3 of 172.3/3 points | Previous AnswersSCalcET7 3.5.001.Consider the following equation.(a) Find by implicit differentiation.which agrees with part (b).3x2y2= (b) Solve the equation explicitly for yand differentiate to get in terms of x.Solution or ExplanationFrom part (a), which agrees with part (b).3x2y2= 9±

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