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5. Evaluate lim -ex + d x -+ 00 x +x Find the horizontal and vertical asymptotes of f(x) = 1+ bx 1 - ax 6. Analyze and sketch the graph of f(x) = - x 3 x2 -25 Be sure to identify the x and y intercepts, find any relative maxima or minima, find any inflection points, find any asymptotes, find the intervals where the function is increasing or decreasing, and find the intervals where the function is concave up or concave down. 7. Find two positive numbers x and y such that x +y = c, c > 0, and the product xy is a maximum. 8. Find the points on the graph of f(x) = x closest to (0,6). 9. Calculate two iterations of Newton's Method to approximate a zero of f(x) = x - 8 using x, =3 as the initial guess. 10. Use differentials to approximate the value of ~ 49-a , writing your answer as a function of a