3 and y 1 (2) Suppose that x = Use five-digit chopping for calculating x + y, x – y,x x y,x ÷ y. Estimate the absolute and relative errors. Use the following table to fill the results. Operation Result Actual Value Absolute Error Relative Error xOy x Ə y x ® y

The standard error of the constant is

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Find y" 3 y = ( 1 +

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Trigonometric Substitution There are certain integrals that contain no trigonometry that can be solved with the aid of trigonometry. Consider integrands involving va? -x, a? +x, or vx - a (where a is constant). These can be evaluated by making the following substitutions. Va? + x x= asin 6 x= atan 0 X= asec 0 dx = acos ede dx = a sec*o de dx = asec Otan ede For each integral, figure out which trigonometric substitution should be used. The goal is to rewrite the integrand so that there is no radical. After integrating, draw and label a right triangle (as shown below). This will allow you to rewrite your integrated expression back in terms of x. For this last part of the problem, you may need one or more trigonometric identities. For example, the triangle that corresponds with exercise 1 looks like this. If we let x = 2sin 0, it follows that sin 6 = x/2. By expressing the side length opposite the given angle as x and the hypotenuse as 2, the side length adjacent the given angle works out…

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11. Evaluate +Vx dx .

In a test drive of a new fuel efficient car, a company tracks the car's mpg (miles per gallon) for 2 gallons of gasoline burned during a test drive. Use the approximating method developed in this section with intervals of 0.25 gallons of gasoline and the "left end" approach to complete the items below. Be sure to indicate the endpoints with open and closed "dots". (Click here for a printable version.)

List the quadrant or quadrants xy > 0 satisfying condition.