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

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Basic Math

Q1). For the function, do the following.

f(x) = 3/x from  a = 1  to  b =2.

(a) Approximate the area under the curve froma to b by calculating a Riemann sum using 10rectangles. 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 tob by evaluating an appropriate definite integral using theFundamental Theorem.

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Q2). According to a study, each additional year ofeducation increases one's income by 17%. Therefore, with xextra years of education, your income will be multiplied by afactor of 1.17x. How many additionalyears of education are required to double your income?That is, find the x that satisfies1.17x = 2. (Round your answer to onedecimal place.)

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Q3). A running track consists of a rectangle with asemicircle at each end, as shown below. If the perimeter is to beexactly 400 yards, find the dimensions (x andr) that maximize the area of the rectangle.[Hint: The perimeter is 2x +2Ï€r.] (Round your answers to the nearestyard.)

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