1.1. Let f(x)= 2+6x—3x?. Then
1.1.1. find the average value of fon [0, 1]
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1.1.2. find a point c on [0, 1] such that f,y. = f(c).
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1.2. | Determine whether the following sequence converges or diverges. If it converges
determine where it converges.
1.2.1 fy
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1.2.2. (F
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1.2.3. fey
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1.3. Let f(x) =e~* . Then determine the third order Taylor polynomial approximation off about
x=0.
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1.4. Let G(x) = fe vi + t* dt. Use the fundamental theorem of calculus to find G’(x).
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1.5. Evaluate the following indefinite integrals.
1.5.1. f ex—e-X dx
[Use integration by substitution]
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eX+e7X
1.5.2. x7? Inx dx
[Use integration by parts.]
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1.6. Evaluate the following definite integrals.
1.6.1. f° (3x? + 2x +5) dx
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2
1.6.2. [rs sin (<) dx
[use integration by substitution.]
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1.7. Determine whether the following series converges or diverges. If it converges find the sum.
1.7.1. E25 (2): - (2))
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1.7.2. Ygco ea(—1)"1
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1.8. Find the interval of convergence and radius of convergence for the power series
Lk=t (pxa-1)*
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1.9. Consider the region enclosed by the curves y = 2x, y = x?.Then