MAT 21C Study Guide - Midterm Guide: Alternating Series

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MAT 21C Full Course Notes

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Make sure that you have all 6 problems. Use series to estimate the following integrals to within 10 8. (cid:90) 0. 1 (a) sin x2 dx. 3: (24 points. ) (a) find the maclaurin polynomial of order 6 for e x. (b) use your answer from part (a) to estimate 1/e. (c) find an upper bound for the error of your estimate in part (b). Let f (x) = x2ex2. (a) find the maclauren series for f (x). (b) find f (7)(0). (c) find f (8)(0). (d) find f (9)(0). Consider the plane that passes through the points (0, 1, 0), (1, 2, 0), and (0, 2, 1). (a) find a vector normal to the plane. (b) find an equation for the plane. Find parametric equations for the line containing (0, 2, 0) and (1, 3, 5). + 5x4 j__ ( l-+ x + )( 1---\-";( 1 c\x. 10-8 to estimate the following integrals to within.

Related Questions

Three Brine Tanks: There are three tanks. Initially the rst tankhas 500 gallons of brine

containing twenty pounds of salt, the second tank contains 200gallons of pure water, and

the third tank contains 1000 gallons of brine containing tenpounds of salt. Brine with a

concentration of 1 lb/gal is poured into the rst tank from anoutside source at a rate of

twenty gallons a second. There are also three tubes connectingthe tanks and they allow

fluids to pass as follows: brine is allowed to move from the rsttank to the second tank

through a tube that allows forty gallons a second to passthrough it, brine is allowed to move

from the second tank to the third tank through a tube thatallows forty gallons a second to

pass through it, and brine is allowed to move from the thirdtank to the rst tank through a

tube that allows twenty gallons a second to pass through it.Lastly, twenty gallons a second

are drained from the third tank and removed from the system.Assume salt is uniformly

distributed within each tank due to stirring.

1. First draw a picture of this situation.

2. Create a model that describes the amount of salt in eachtank at time t.

3. Solve the model. You will need to look at section 5.6 tolearn how to deal with a

nonhomogeneous linear system.

4. Plot your solutions on the same graph (you should havethree equations that you plot

against time t).

5. When does the concentration of the salt in the second tankreach 0:5 pounds a gallon?

6. What quantity of salt will each tank be nearing as t getslarge? How could we have

known this without even building a model?

PLEASE ANSWER ALL. I donât understand my teachers explanations.

MAT 21C Study Guide - Midterm Guide: Alternating Series

MAT 21C Full Course Notes

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