Department

MathematicsCourse Code

MAT 145Professor

AllStudy Guide

MidtermThis

**preview**shows half of the first page. to view the full**1 pages of the document.**MAT 145 Term Test 5

2012 Spring

1. Determine the exact value of the definite integral (5 + 6+12

) .

2. A particle moves along the horizontal axis with acceleration ()= 2, 0 10. We also

know the initial velocity,

a) Determine v(t), a function for the velocity

b) Calculate the total distance traveled by the particle for 0 10.

3. If ()=cos(3)

, determine g’(x).

4. Evaluate

.

5. We know that () =6, () =14,() =23.

Determine ().

6. Use Riemann Sum to approximate the area under the curve ()=

, 0 2, using n=4

subdivisions and the midpoint method. Round to the nearest thousandth.

7. Let g(t) represent a child’s rate of growth in pounds per year. Write a definite integral to

represent the change in the child’s weight, in pounds from year 4 to year 9.

8. An animal population is increasing at a rate of ()= 4 + 29 animals per year, t measured in

years. By how many animals does the population increase from year 3 to year 7?

9. A particle moves along the horizontal axis with velocity ()= 3 3, 0 6, measured in

ft/s. Determine the net change in position of the particle on 0≤t≤6.2

10. We wish to create a Riemann Sum to approximate the area under the curve =+ 2, 1

2, using n=4 subdivisions and the left-endpoint method.

a) Create a picture to show the function and the approximating rec tangles. Clearly label

the elements of your picture, including the function the horizontal axis scale, any x-axis

tick marks and your rectangles.

b) Write an expression, showing all terms, to represent the Reimann Sum.

c) Calculate the exact value, expressed as a common fraction, for this Riemann Sum.

Bonus!

Let R be the first-quadrant region bounded by the x-axis, the y-axis, and the graph of = 4 .

Determine the smallest number of subdivisions we must use in a left-endpoint Riemann Sum in order

to approximate the actual area of R with error no more than 0.01. Describe your process, justification

and results.

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