# 15 multiple choice calc 1

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1.

Which of the following is the general solution of the differential equation ? (4 points)

2.

The slope of the tangent line to a curve at any point (x, y) on the curve is . 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 for which y(0) = 80 is (4 points)

4.

The temperature of a roast varies according to Newton’s Law of Cooling: , where T is the roast temperature, A is the room temperature, and k is a positive constant.

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

5.

Find the specific solution of the differential equation with condition y(-4) = *e*. (4 points)

1.

Choose the appropriate table for the differential equation . (4 points)

2.

A slope field produces (4 points)

3.

The differential equation . (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?

(4 points)

5.

The differential equation . (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 ? (4 points)

2.

Which definite integral approximation formula is ? (4 points)

3.

The estimated value of , 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

. (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 Which one of the following statements is true? (4 points)

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