w07e - W (-2) and W (-2)? d) Explain the relationships...

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Math 151, Workshop 7 1. The graph of the tilted ellipse x 2 - xy + y 2 = 3 is shown to the right. What are the dimensions and the location of the box containing the ellipse? Note. The sides of the box are vertical and horizontal and also are tangent to the ellipse. -1.2 1.2 1.6 0.4 -0.4 0 x y 0.8 0 0.4 0.8 2 1.2 -0.8 2. Find the largest circle centered on the posi- tive y -axis which touches the origin and which is above y = x 2 . 3. De±ne: Z ( x ) = 3 x - 5 2 x - 1 . a) Compute Z ( x ). What are Z (1) and Z (1)? b) Suppose s is any number in the domain of Z , and t = Z ( s ). Solve this equation for s . Explain why solving this equation veri±es that Z is one-to-one. c) Find W , the function inverse to Z , and compute W . What are
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Unformatted text preview: W (-2) and W (-2)? d) Explain the relationships between the numerical answers in a) and c). 4. It is true that Q ( x ) = x 5 + x 3 + x is a one-to-one function whose domain and range are all real numbers? a) Graph Q ( x ) on the interval-2 x 2. b) Suppose that R is the function inverse to Q . There is no simple algebraic way to compute values of R . Compute R (3), R (3) and R (3). Hint. Q ( R ( x )) = x and R ( Q ( x )) = x . Find an input to Q which will output 3. Then dierentiate one of the equations (maybe more than once)....
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