This Set of Problems Is for Preparing for the Final Exam of Math 190

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This set of problems is for preparing for the final exam of Math 190.

You need to do more problems in order to perform well on the test.

1.  Use a graph to find a number δ such that whenever.

2.  If for all x, find.

3.  (a) Use the definition of derivative to find the slope of the tangent line to the

graph of the exponential function at the point (0,1).

(b) Estimate the slope to three decimal places.

4.  Use the midpoint rule with n = 4 to approximate the area of the region bounded by the given curves. .

5.  Find the area of the region bounded by the parabola, the tangent line to this parabola at (6,36), and the x-axis.

6.  Evaluate the integral.

7.  If , where , find

8.  Find the inflection point for the function.

9.  Use Newton’s method with the initial approximation =2 to find, the fourth approximation to the root of the equation.(Give your answer to four decimal places.)

10.  Consider the figure below, where AC = 7 ft, BD = 1ft and AB = 6 ft. How far from the point A should the point P be chosen on the line segment AB so as to maximize the angle θ? Round you answer to the nearest hundredth.

11.  Evaluate the limit.

12.  Use implicit differentiation to find an equation of the tangent line to the curve at the point (1,1).

13.  Find the limit.

14.  Find the exact values of the numbers c that satisfy the conclusion of The Mean Value Theorem for the function for the interval [-5,5].

15.  Find .

16.  The velocity of a particle is. Compute the

(a)  displacement over [0,4], [4,6], and [0,6].

(b)  Total distance traveled over [0,6].

17.  Find.

18.  It costs you c dollars each to manufacture and distribute backpacks. If the backpacks sell at x dollars each, the number sold is given by where a and b are positive constants. What selling price will bring a maximum profit?