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mathematics
precalculus

Questions and Answers of Precalculus

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If f (x) = 2x - x2 + 1/3 x3 - ∙ ∙ ∙
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If ∑an is divergent, then ∑|an| is
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If 0 < an < bn and ∑bn diverges, then
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.The Ratio Test can be used to determine
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.The Ratio Test can be used to determine
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If ∑cnxn diverges when x = 6, then it
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If ∑cnxn is convergent, then ∑cn(-6)n is
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If ∑cnxn is convergent, then ∑cn(-2)n is
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. = L. If lim,. an = L, then lim,,→. A2n+1
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.The seriesis convergent. -sin 1 n- n-1 n
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. If lim,. an = 0, then E a, is convergent. n
Determine whether the series converges or diverges. Σ n-1 νn2 +1 n=1
Use the Integral Test to determine whether the series is convergent or divergent. ο0 Σnfen ,3 -n- n=1
Use the Integral Test to determine whether the series is convergent or divergent. Σ (Зп — 1)* п31
Use the Integral Test to determine whether the series is convergent or divergent. Σ 5n – 1 п3
Use the Integral Test to determine whether the series is convergent or divergent.
Use the Integral Test to determine whether the series is convergent or divergent. ο0 ΣΤ -3 η η-1 Π
Suppose f is a continuous positive decreasing function for x > 1 and an = f (n). By drawing a picture, rank the following three quantities in increasing order: 6 9. Γωα Σαι aι |f(x) dx Σ
The Fibonacci sequence was defined in Section 11.1 by the equationsShow that each of the following statements is true.(a)(b)(c) fi = 1, f = 1, fa = fa-1 + fn-2 %3D 1 fa-1 fn+1 fa-1 fa fn fa+1
Suppose that a series o an has positive terms and its partial sums sn satisfy the inequality sn < 1000 for all n. Explain why ∑an must be convergent.
If o an and ∑an are both divergent, is ∑ (an + bn) necessarily divergent?
If ∑an is convergent and ∑bn is divergent, show that the series ∑ (an + bn) is divergent.
Suppose that is known to be a convergentseries. Prove that is a divergent series. ( α. - 0) ΣΤ-1 a, a, 0) E-1 1/a, n=1
A patient is injected with a drug every 12 hours. Immediately before each injection the concentration of the drug has been reduced by 90% and the new dose increases the concentration by 1.5 mg/L.(a)
A doctor prescribes a 100-mg antibiotic tablet to be taken every eight hours. Just before each tablet is taken, 20% of the drug remains in the body.(a) How much of the drug is in the body just after
If the nth partial sum of a seriesSn = n - 1 / n + 1find an and En-1 an is Σ п — 1 п +1 Sn п
Use the partial fraction command on your CAS to find a convenient expression for the partial sum, and then use this expression to find the sum of the series. Check your answer by using the CAS to sum
Find the values of x for which the series converges. Find the sum of the series for those values of x. α Σ(-4)"(x-5)" n-0
Find the values of x for which the series converges. Find the sum of the series for those values of x. en п-0 пх
Find the values of x for which the series converges. Find the sum of the series for those values of x. sin"x 3" n-0
Find the values of x for which the series converges. Find the sum of the series for those values of x. Σ (1+ (x + 2)' n-1
Find the values of x for which the series converges. Find the sum of the series for those values of x. E (-5)"x" п-1
Express the number as a ratio of integers.5.7̅1̅3̅5̅8̅
Express the number as a ratio of integers.1.2345̅6̅7̅
Express the number as a ratio of integers.10.̅135̅= 10.135353535 . . .
Express the number as a ratio of integers.0.̅8 − 0.8888 . . .
A sequence of terms is defined bya1 = 1 an = (5 - n)an-1Calculate En=1 An.
Determine whether the series is convergent or divergent by expressing sn as a telescoping sum (as in Example 8). If it is convergent, find its sum. 1 Σ пз — п п-2 пз
Determine whether the series is convergent or divergent by expressing sn as a telescoping sum (as in Example 8). If it is convergent, find its sum. E (em – e'/n+1) n-1
Determine whether the series is convergent or divergent by expressing sn as a telescoping sum (as in Example 8). If it is convergent, find its sum. Σ n=4 /n Vn + 1
Determine whether the series is convergent or divergent by expressing sn as a telescoping sum (as in Example 8). If it is convergent, find its sum. 3 Σ п(п + 3) п—1
Determine whether the series is convergent or divergent by expressing sn as a telescoping sum (as in Example 8). If it is convergent, find its sum. п Ση In п+1 п-1
Determine whether the series is convergent or divergent. If it is convergent, find its sum.
Determine whether the series is convergent or divergent. If it is convergent, find its sum.
Determine whether the series is convergent or divergent. If it is convergent, find its sum.
Determine whether the series is convergent or divergent. If it is convergent, find its sum. 2 arctan n n-1
Determine whether the series is convergent or divergent. If it is convergent, find its sum. Σ ()* -k k-0
Determine whether the series is convergent or divergent. If it is convergent, find its sum. n? + 1 Σ n 2n2 + 1 n=1
Determine whether the series is convergent or divergent. If it is convergent, find its sum.
Determine whether the series is convergent or divergent. If it is convergent, find its sum. 2 (sin 100)* k-1
Determine whether the series is convergent or divergent. If it is convergent, find its sum.
Determine whether the series is convergent or divergent. If it is convergent, find its sum. 1 n-1 4 + e-n
Determine whether the series is convergent or divergent. If it is convergent, find its sum. E [(-0.2)" + (0.6)"-1] n=1
Determine whether the series is convergent or divergent. If it is convergent, find its sum. +14° У 31+14-я —п п-1
Determine whether the series is convergent or divergent. If it is convergent, find its sum. k? Σ そミ k? – 2k + 5 k=1
Determine whether the series is convergent or divergent. If it is convergent, find its sum. 2 + n Σ 1- 2n n-1 8
Determine whether the series is convergent or divergent. If it is convergent, find its sum. 1 3 9. 27 729 81 243
Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum.
Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum.
Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum.
Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum.
Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum. п TT п-
Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum.
Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum.2 + 0.5 + 0.125 + 0.03125 + ∙ ∙ ∙
Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum.10 - 2 + 0.4 - 0.08 + ∙ ∙ ∙
Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum. 4 + 3 + ? + + .. 27 16
Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum. 16 |3 – 4 + - +
(a) Explain the difference between(b) Explain the difference between Π Σ α and aj j-1 ai η Σ α1 i-1 aj and i-1
Let an = 2n/3n + 1.(a) Determine whether {an} is convergent.(b) Determine whether an is convergent. 00 2n=1 an
Find at least 10 partial sums of the series. Graph both the sequence of terms and the sequence of partial sums on the same screen. Does it appear that the series is convergent or divergent?If it is
Find at least 10 partial sums of the series. Graph both the sequence of terms and the sequence of partial sums on the same screen. Does it appear that the series is convergent or divergent?If it is
Find at least 10 partial sums of the series. Graph both the sequence of terms and the sequence of partial sums on the same screen. Does it appear that the series is convergent or divergent?If it is
Find at least 10 partial sums of the series. Graph both the sequence of terms and the sequence of partial sums on the same screen. Does it appear that the series is convergent or divergent?If it is
Find at least 10 partial sums of the series. Graph both the sequence of terms and the sequence of partial sums on the same screen. Does it appear that the series is convergent or divergent?If it is
Find at least 10 partial sums of the series. Graph both the sequence of terms and the sequence of partial sums on the same screen. Does it appear that the series is convergent or divergent?If it is
Calculate the first eight terms of the sequence of partial sums correct to four decimal places. Does it appear that the series is convergent or divergent? (-1)*-1 п! п—1
Calculate the first eight terms of the sequence of partial sums correct to four decimal places. Does it appear that the series is convergent or divergent? E sin n n-1
Calculate the first eight terms of the sequence of partial sums correct to four decimal places. Does it appear that the series is convergent or divergent? 1 п п-1
Calculate the first eight terms of the sequence of partial sums correct to four decimal places. Does it appear that the series is convergent or divergent? Σ n* + n? п—1
Calculate the sum of the series an whose partial sums are given. n=1 An n2 – 1 + 1 Sn 4n2
Calculate the sum of the series an whose partial sums are given. n=1 An
Explain what it means to say that 2 n=1 An n=1 An = 5.
Prove Theorem 6.Use either Definition 2 or the Squeeze Theorem.
Use Definition 2 directly to prove that limn →∞ rn = 0 when |r| < 1.
Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?an = n3 - 3n + 3
Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?an = 3 - 2ne-n
Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?an = 2 + (-1)n/n
Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?an = n(-1)n
Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?an = 1- n/2 + \n
Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?an = 1/2n + 3
Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?an = cos n
If you deposit $100 at the end of every month into an account that pays 3% interest per year compounded monthly, the amount of interest accumulated after n months is given by the sequence
(a) Determine whether the sequence defined as follows is convergent or divergent:a1 = 1 an + 1 = 4n an for n > 1(b) What happens if the first term is a1 = 2?
Use a graph of the sequence to decide whether the sequence is convergent or divergent. If the sequence is convergent, guess the value of the limit from the graph and then prove your guess.
Use a graph of the sequence to decide whether the sequence is convergent or divergent. If the sequence is convergent, guess the value of the limit from the graph and then prove your guess.
Use a graph of the sequence to decide whether the sequence is convergent or divergent. If the sequence is convergent, guess the value of the limit from the graph and then prove your guess. (See the
Use a graph of the sequence to decide whether the sequence is convergent or divergent. If the sequence is convergent, guess the value of the limit from the graph and then prove your guess. (See the
Use a graph of the sequence to decide whether the sequence is convergent or divergent. If the sequence is convergent, guess the value of the limit from the graph and then prove your guess. (See the

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