Consider the following. x² + y2 = 16 %3D (a) Find two explicit functions by solving the equation for y in terms of x. Y1= (positive function) Y2 = (negative function) (b) Sketch the graph of the equation and label the parts given by the corresponding explicit functions. y y 5 -5 y y 5 X 5 -5

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Consider the following.
x² + y2 :
= 16
(a) Find two explicit functions by solving the equation for y in terms of x.
Y =
(positive function)
Y2 =
(negative function)
(b) Sketch the graph of the equation and label the parts given by the
corresponding explicit functions.
y
y
5
X
-5
-5
y
y
5
5
-5
-5
(c) Differentiate the explicit functions.
dy/dx = +
(d) Find dy/dx through implicit differentiation.
dy/dx =
y
Is the result equivalent to that of part (c)?
Yes
No
O O
Transcribed Image Text:Consider the following. x² + y2 : = 16 (a) Find two explicit functions by solving the equation for y in terms of x. Y = (positive function) Y2 = (negative function) (b) Sketch the graph of the equation and label the parts given by the corresponding explicit functions. y y 5 X -5 -5 y y 5 5 -5 -5 (c) Differentiate the explicit functions. dy/dx = + (d) Find dy/dx through implicit differentiation. dy/dx = y Is the result equivalent to that of part (c)? Yes No O O
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