Question

Q1). Find (without using a calculator) the absolute extreme values of the function on the given interval.

f(x)= x/x^2+9 on [-5,5]

(find absolute minimum and absolute maximum)

Q2). 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.)

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Q3). The number x of printer cartridges that a store will sell per week and their price p (in dollars) are related by the equation x² = 2520 − 5p². If the price is falling at the rate of $1 per week, find how the sales will change if the current price is $18.

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Q4). Find the value of $1200 deposited in a bank at 10% interest for 10 years compounded in the following ways. (Round your answers to the nearest cent)

a). annually

b). quarterly

c). continuously

Q5). The cost of a four-year private college education (after financial aid) has been estimated to be $50,000.† How large a trust fund, paying 4% compounded quarterly, must be established at a child's birth to ensure sufficient funds at age 18? (Round your answer to the nearest cent.)

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Q6). A bank offers 6% compounded continuously. How soon will a deposit do the following? (Round your answers to one decimal place.)

(a) triple

(b) increase by 23%

Q7). 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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Q8). 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.

Answer 1