Math 149 Lab 3 - ExercisesName: < your name goes here >Section: < your section goes here >Instructions for Exercises 1 and 2ü (a) Plot a graph of the equation E(x,y)ü (b) Verify that the point P is on the graphü (c) Find dy/dx implicitly with Mathematica.ü (d) Find the slope of the tangent line to the curve at Pü (3) Plot the curve and and the tangent line on the same set of axes.Exercise 1ü Sinx y y2Cosx, for x in [ -1.5, 1.5 ], and y in [-4, 4] with point P(0,0).Exercise 2ü y4x2 y2, for x in [ -1, 1 ] and y in [-1, 1] with point P ( 34 , 32 )ü Solve the equation for y . There will be four (4) solutions, each a function of x. Determine which part of the graph of the equation is the graph of each ofthese four functions. Plot all four solutions on the same graph in different colors.Instructions for Exercise 3 and 4Let g denote the inverse of f.ü Plot f, g, and the identity function j(x) = x.Include in your plot a label for the two curves: y = f(x) and y = g(x).ü Plot a graph of g and gx in the same coordinate plane. ü Find a formula for the derivative gx in terms of x and g[x].Exercise 3ü fx 1 x x2 x3 for x in [ -1, 3/2 ]Find g2.Exercise 4ü f[x]ä x + Sin[x] for x in [ 3 4 , 3 4 ]Find g1 2.2 Math 149 Lab 3
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