1.

Which of the following is the general solution of the differential equation dy dx equals the quotient of 4 times x and y ? (4 points)

2.

The slope of the tangent line to a curve at any point (x, y) on the curve is x divided by y . What is the equation of the curve if (4, 1) is a point on the curve? (4 points)

3.

The particular solution of the differential equation dy dt equals y over 2 for which y(0) = 80 is (4 points)

4.

The temperature of a roast varies according to Newton’s Law of Cooling: dT dt equals negative k times the quantity T minus A , where T is the roast temperature, A is the room temperature, and k is a positive constant.

If a room temperature roast cools from 68°F to 25°F in 5 hours at freezer temperature of 20°F, how long (to the nearest hour) will it take the roast to cool to 21°F? (4 points)

5.

Find the specific solution of the differential equation dy dx equals the quotient of 4 times y and x squared with condition y(-4) = e. (4 points)

1.

Choose the appropriate table for the differential equation dy dx equals the quotient of the quantity x plus 2 and x . (4 points)

2.

A slope field produces (4 points)

3.

The differential equation dy dx equals the quotient of x and x minus 4. (4 points)

I. will have a slope field with negative slopes in quadrant I
II. will have a slope field with positive slopes in all quadrants
III. will produce a slope field with columns of parallel tangents

4.

Which of the following differential equations is consistent with the following slope field?

In quadrant one, all slopes are positive. Greater values of y have slopes approaching horizontal and y less than 1 have slopes approaching vertical. For quadrant two slopes are negative with slopes approaching horizontal for greater values of y. Quadrant three also has all negative slopes. Larger negative values of y have slopes approaching horizontal. All slopes are positive in quadrant four. (4 points)

5.

The differential equation dy dx equals the quotient of the quantity y minus 3 and x minus 3. (4 points)

I. produces a slope field with horizontal tangents at y = 3
II. produces a slope field with vertical tangents at y = 3
III. produces a slope field with rows of parallel segments

1.

Which of the following values would be obtained using 10 inscribed rectangles of equal width (a lower sum) to estimate the integral from 0 to 1 of x squared, dx ? (4 points)

2.

Which definite integral approximation formula is the integral from a to b of f of x, dx is approximately equal to the product of the quantity b minus a over 2 times n and the quantity y sub 0 plus 2 times y sub 1 plus 2 times y sub 2 plus 2 times y sub 3 plus dot dot dot plus 2 times y sub n minus 1 plus y sub n ? (4 points)

3.

The estimated value of the integral from 0 to 2 of x cubed dx , using the trapezoidal rule with 4 trapezoids is (4 points)

4.

Given the table below for selected values of f(x), use 6 right rectangles to estimate the value of

the integral from 1 to 10 of f of x dx . (4 points)

x 1 3 4 6 7 9 10
f(x) 4 8 6 10 10 12 16

5.

Function f(x) is positive, increasing and concave down on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the left sum, right sum, and trapezoidal rule approximations for the value of the integral from a to b of f of x dx Which one of the following statements is true? (4 points)

 

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