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MSU MTH 132 - Instruction Notes

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NOTES FOR MTH 132INSTRUCTORS1. In Section 2.2 use the Sandwich Theorem to show that limx→0x sin1x= 0.2. From Section 2.3 cover only the formal definition of limit. In class do evenproblems from the supplemental exercises.3. There is a shortage of exercises at the end of Section 2.4 concerning theformula limx→0sin xx= 1. Additional problems are in the SupplementalExercises for Section 2.4.4. In Section 2.4 mention that the Sandwich Theorem holds for limits at±∞.5. When covering Section 2.6 do problems 3 and 6 from the SupplementalExercises for Section 2.6.6. Omit Section 2.7. It is superseded by Section 3.1.7. In Section 2.2 state the formula for computing the product of three andmore factors. Examples can be given after Section 3.4.8. Demonstrate the formula for the derivative of the product of three factorsusing the trig functions introduced in Section 3.4. Repeat in the nextsection.9. Replace the proof of the Power Rule for Rational Exponents in Section3.6 with the one presented in the Supplemental Material for Section 3.6.10. The textbook is short on exercises to find the line tangent to the graph ofan equation at a point on the graph. In the Supplemental Exercises forSection 3.6 you will find some additional problems.11. The definition of local extreme values in the textbook is not clear. Statethe definition so that it is clear that a local extreme value can’t occur atan endpoint.12. The textbook seems to miss the point of linear approximation (Section3.8). Point out that it is just the first step. In second semester calculusapproximation by higher degree polynomials is presented. When coveringSection 3.7 do problems such as, “Approximate√8.5,√17,3√26 etc”.113. The text neglects to mention that l’Hˆopital’s rule holds when x → ±∞.The first 8 problems and many others on page 298 can be done moreefficiently by methods other than l’Hˆopitals Rule. So select problems todo in class with care.14. In Section 4.8, page 308 amend the formula 4. - 7. as follows.Function General antiderivativesec2(kx)tan(kx)k+ Ccsc2(kx) −cot(kx)k+ Csec(kx) tan(kx)sec(kx)k+ Ccsc(kx) cot(kx) −csc(kx)k+ C15. For Section 5.3 use the Supplemental Material for Section 5.3 to presentthe definite (Riemann) Integral. For average value, see the textbook, butthe assumption of continuity isn’t necessary. Change it to


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MSU MTH 132 - Instruction Notes

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