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mathematics
precalculus 1st

Questions and Answers of Precalculus 1st

Find the limit of the following sequences or determine that the limit does not exist. {tan ¹n}
Evaluate the following geometric sums. 20 Σ(-1)* k=0
Find the limit of the following sequences or determine that the limit does not exist. {csc ¹n}
Evaluate the following geometric sums. + 419 + 1 +
Evaluate the geometric series or state that it diverges. |
Find the limit of the following sequences or determine that the limit does not exist. {.(i)}
Evaluate the geometric series or state that it diverges. 00 Σε k=1 ₂-2k
Find the limit of the following sequences or determine that the limit does not exist. {(₁-4)²} n
Evaluate the geometric series or state that it diverges. 00 m=2 5 2m
Find the limit of the following sequences or determine that the limit does not exist. {bn} where bn [n/(n + 1) ifn ≤ 5000 [ne-n if n > 5000
Evaluate the geometric series or state that it diverges. 00 Σ2-3* k=1
Find the limit of the following sequences or determine that the limit does not exist. n {(₁ + ²)"}
Find the limit of the following sequences or determine that the limit does not exist. n 1 {√(1 + 2)"} 2n
Find the limit of the following sequences or determine that the limit does not exist. {(n + 5)²}
Write the first four terms of the sequence {an} defined by the following recurrence relations. an+1 = a₁2² - 1; a₁ = 1 an
Write the first four terms of the sequence {an} defined by the following recurrence relations. an+1 = 2 3a²+n+ 1; a₁ = 0
Find the limit of the following sequences or determine that the limit does not exist. Зи {(₁ -A)³} 1 + n
Write the first four terms of the sequence {an} defined by the following recurrence relations. an+1 = anan-1; a₁ = 1, ao = 1
Evaluate the geometric series or state that it diverges. 8 00 k=0 2k 二 75
Find the limit of the following sequences or determine that the limit does not exist. n en + 3n
Evaluate the geometric series or state that it diverges. 00 k=0 1.01k
Find the limit of the following sequences or determine that the limit does not exist. In (1/n) n
Several terms of a sequenceare given.a. Find the next two terms of the sequence.b. Find a recurrence relation that generates the sequence (supply the initial value of the index and the first term of
Evaluate the geometric series or state that it diverges. 8 00 k=3 3.4k 가
Find the limit of the following sequences or determine that the limit does not exist. {In sin (1/n) + In n}
Find the limit of the following sequences or determine that the limit does not exist. {In (n³ + 1) In (3n³ + 10n)}
Several terms of a sequenceare given.a. Find the next two terms of the sequence.b. Find a recurrence relation that generates the sequence (supply the initial value of the index and the first term of
Evaluate the geometric series or state that it diverges. -| 1 k=45k
Several terms of a sequenceare given.a. Find the next two terms of the sequence.b. Find a recurrence relation that generates the sequence (supply the initial value of the index and the first term of
Find the limit of the following sequences or determine that the limit does not exist. {n sin (6/n)}
Find the limit of the following sequences or determine that the limit does not exist. {((u/1) sox - 1)u}
Evaluate the geometric series or state that it diverges. k=0 3. -k
Evaluate the geometric series or state that it diverges. E | نه 8
Find the limit of the following sequences or determine that the limit does not exist. [(-1)" n
Evaluate the geometric series or state that it diverges. 00 k=1 3k-1 4k+1
Find the limit of the following sequences or determine that the limit does not exist. S(-1)^²+1 n²) 2n³ + n
Find the limit of the following sequences or determine that the limit does not exist. [(-1)^n) n + 1.
Evaluate the geometric series or state that it diverges. k=0 9 10, k
Evaluate the geometric series or state that it diverges. 8 k=0 4) 56-k
Evaluate the geometric series or state that it diverges. 3k m 100
Evaluate the geometric series or state that it diverges. k=1 al 3 k
Write the terms a1, a2, a3, and a4 of the following sequences. If the sequence appears to converge, make a conjecture about its limit. If the sequence diverges, explain why. an+1 = 1 + an 2 0 = 2
Evaluate the geometric series or state that it diverges. 3Σ (-1)k k k=0 TT
Write the terms a1, a2, a3, and a4 of the following sequences. If the sequence appears to converge, make a conjecture about its limit. If the sequence diverges, explain why. an+1 = 1-an; ao = 1/
Evaluate the geometric series or state that it diverges. 00 Σ(e)* k=1 k
Write the terms a1, a2, a3, and a4 of the following sequences. If the sequence appears to converge, make a conjecture about its limit. If the sequence diverges, explain why. an+1 = 0.5an + 50; ao 100
Evaluate the geometric series or state that it diverges. 00 Σ(-0.15) k=2
Find the limit of the following sequences or determine that the limit does not exist. Verify your result with a graphing utility. an || e-n е 2 sin (e")
Evaluate the geometric series or state that it diverges. 3k I=Y 8 (†-)&
Write each repeating decimal first as a geometric series and then as a fraction (a ratio of two integers). 0.3 = 0.333...
Find the limit of the following sequences or determine that the limit does not exist. Verify your result with a graphing utility. an = encos n
Write each repeating decimal first as a geometric series and then as a fraction (a ratio of two integers). 0.6 = 0.666...
Find the limit of the following sequences or determine that the limit does not exist. Verify your result with a graphing utility. In n 1.1. n
Write each repeating decimal first as a geometric series and then as a fraction (a ratio of two integers). 0.1 = 0.111...
Write each repeating decimal first as a geometric series and then as a fraction (a ratio of two integers). 0.5 = 0.555...
Find the limit of the following sequences or determine that the limit does not exist. Verify your result with a graphing utility. an = cot NTT 2n + 2
Find the limit of the following sequences or determine that the limit does not exist. Verify your result with a graphing utility. an = (-1)" Wn
Determine whether the following sequences converge or diverge and describe whether they do so monotonically or by oscillation. Give the limit when the sequence converges. {0.2"}
Write each repeating decimal first as a geometric series and then as a fraction (a ratio of two integers). 0.09 = 0.090909..
Write each repeating decimal first as a geometric series and then as a fraction (a ratio of two integers). 0.27 0.272727...
Consider the formulas for the following sequences. Using a calculator, make a table with at least 10 terms and determine a plausible value for the limit of the sequence or state that it does not
Write each repeating decimal first as a geometric series and then as a fraction (a ratio of two integers). 0.037 0.037037...
Determine whether the following sequences converge or diverge and describe whether they do so monotonically or by oscillation. Give the limit when the sequence converges. {1.2"}
Determine whether the following sequences converge or diverge and describe whether they do so monotonically or by oscillation. Give the limit when the sequence converges. {(-0.7)"}
Write each repeating decimal first as a geometric series and then as a fraction (a ratio of two integers). 0.12 = 0.121212...
Write each repeating decimal first as a geometric series and then as a fraction (a ratio of two integers). 0.027 = 0.027027..
Determine whether the following sequences converge or diverge and describe whether they do so monotonically or by oscillation. Give the limit when the sequence converges. {(-1.01)"}
Write each repeating decimal first as a geometric series and then as a fraction (a ratio of two integers). 1.25 = 1.252525...
Determine whether the following sequences converge or diverge and describe whether they do so monotonically or by oscillation. Give the limit when the sequence converges. {2" 3"}
Squeeze Theorem Find the limit of the following sequences or state that they diverge.Data from in Squeeze Theorem sin 6n 5n
Squeeze Theorem Find the limit of the following sequences or state that they diverge.Data from in Squeeze Theorem cos n n
Consider the following recurrence relations. Using a calculator, make a table with at least 10 terms and determine a plausible value for the limit of the sequence or state that it does not exist.
Squeeze Theorem Find the limit of the following sequences or state that they diverge.Data from in Squeeze Theorem sin n 2"
For the following telescoping series, find a formula for the nth term of the sequence of partial sums {Sn}. Then evaluate to obtain the value of the series or state that the series diverges. lim
Squeeze Theorem Find the limit of the following sequences or state that they diverge.Data from in Squeeze Theorem [cos (nπ/2)) Vn
For the following telescoping series, find a formula for the nth term of the sequence of partial sums {Sn}. Then evaluate to obtain the value of the series or state that the series diverges. lim
Determine whether the following sequences converge or diverge and describe whether they do so monotonically or by oscillation. Give the limit when the sequence converges. {(-2.5)"}
Squeeze Theorem Find the limit of the following sequences or state that they diverge.Data from in Squeeze Theorem 2 tan n n³ + 4
Squeeze Theorem Find the limit of the following sequences or state that they diverge.Data from in Squeeze Theorem 'n sin³ n {n+1]
Consider the following recurrence relations. Using a calculator, make a table with at least 10 terms and determine a plausible value for the limit of the sequence or state that it does not exist.
Consider the following recurrence relations. Using a calculator, make a table with at least 10 terms and determine a plausible value for the limit of the sequence or state that it does not exist.
For the following telescoping series, find a formula for the nth term of the sequence of partial sums {Sn}. Then evaluate to obtain the value of the series or state that the series diverges. lim
Use Theorem 9.6 to find the limit of the following sequences or state that they diverge.Data from in Theorem 9.6 n! n
For the following telescoping series, find a formula for the nth term of the sequence of partial sums {Sn}. Then evaluate to obtain the value of the series or state that the series diverges. lim
Use the formal definition of the limit of a sequence to prove the following limits.Data from in Definition 1 lim = 0 n-00 n
Use the formal definition of the limit of a sequence to prove the following limits.Data from in Definition lim = 0 1 2 n→∞ n
Evaluate the series or state that it diverges. 00 In((k + 1)k-¹) (Ink) In (k + 1)
Use Theorem 9.6 to find the limit of the following sequences or state that they diverge.Data from in Theorem 9.6 1000 n {12} n 2"
For the following telescoping series, find a formula for the nth term of the sequence of partial sums {Sn}. Then evaluate to obtain the value of the series or state that the series diverges. lim
For the following telescoping series, find a formula for the nth term of the sequence of partial sums {Sn}. Then evaluate to obtain the value of the series or state that the series diverges. lim
Use Theorem 9.6 to find the limit of the following sequences or state that they diverge.Data from in Theorem 9.6 n 10 In ¹000 n
For the following telescoping series, find a formula for the nth term of the sequence of partial sums {Sn}. Then evaluate to obtain the value of the series or state that the series diverges. lim
Use Theorem 9.6 to find the limit of the following sequences or state that they diverge.Data from in Theorem 9.6 n10 In 20 n
For the following telescoping series, find a formula for the nth term of the sequence of partial sums {Sn}. Then evaluate to obtain the value of the series or state that the series diverges. lim
Use Theorem 9.6 to find the limit of the following sequences or state that they diverge.Data from in Theorem 9.6 3n n!
Consider the following infinite series.a. Write out the first four terms of the sequence of partial sums.b. Estimate the limit of {Sn} or state that it does not exist. 00 Σ (1)* k=1
Use the formal definition of the limit of a sequence to prove the following limits.Data from in Definition си lim no bn + 1 C for real numbers c> 0 and b > 0 b'
Consider the following infinite series.a. Write out the first four terms of the sequence of partial sums.b. Estimate the limit of {Sn} or state that it does not exist. Σ (-1)* κ k=1
Consider the following infinite series.a. Write out the first four terms of the sequence of partial sums.b. Estimate the limit of {Sn} or state that it does not exist. 00 k= 3 10k
Evaluate the limit of the following sequences. an || n [x 1 x-² dx

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