Math 149 Lab 3 Exercises Name your name goes here Section your section goes here Instructions for Exercises 1 and 2 a Plot a graph of the equation E x y b Verify that the point P is on the graph c Find dy dx implicitly with Mathematica d Find the slope of the tangent line to the curve at P 3 Plot the curve and and the tangent line on the same set of axes Exercise 1 Sin x y y2 Cos x for x in 1 5 1 5 and y in 4 4 with point P 0 0 Exercise 2 y4 x2 y2 for x in 1 1 and y in 1 1 with point P 3 4 3 2 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 of these four functions Plot all four solutions on the same graph in different colors Instructions for Exercise 3 and 4 Let g denote the inverse of f 2 Math 149 Lab 3 Exercises nb 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 Plot a graph of g and g x in the same coordinate plane Find a formula for the derivative g x in terms of x and g x Exercise 3 f x 1 x x2 x3 for x in 1 3 2 Find g 2 Exercise 4 f x x Sin x for x in 34 Find g 1 2 3 4
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