Q1). For the function, do the following. f(x) = 3/x from a = 1 to b = 2. (a)...

Q1). For the function, do the following.

f(x) = 3/x from a = 1 to b = 2.

(a) Approximate the area under the curve from a to b by calculating a Riemann sum using 10 rectangles. Use the method described in Example 1 on page 351, rounding to three decimal places.

(b) Find the exact area under the curve from a to b by evaluating an appropriate definite integral using the Fundamental Theorem.

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Q2). According to a study, each additional year of education increases one's income by 17%. Therefore, with x extra years of education, your income will be multiplied by a factor of 1.17^x. How many additional years of education are required to double your income? That is, find the x that satisfies 1.17^x = 2. (Round your answer to one decimal place.)

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Q3). A running track consists of a rectangle with a semicircle at each end, as shown below. If the perimeter is to be exactly 400 yards, find the dimensions (x and r) that maximize the area of the rectangle. [Hint: The perimeter is 2x + 2πr.] (Round your answers to the nearest yard.)

Expert Solution

milcah answered 2 years ago

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