n2 -5n +4 an 3n2 +5 n-1 Vn=6n- 3 4 %D Wn = 4 %D -/3 II

Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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### Mathematical Sequence Problems

1. Determine the limit as \( n \) approaches infinity for the given sequence \( q_n \):

\[ q_n = \frac{n^2 - 5n + 4}{3n^2 + 5} \]

\[ = \quad [?] \quad \boxed{0} \]

2. Determine the limit as \( n \) approaches infinity for the given sequence \( b_n \):

\[ b_n = 4 \left( \frac{1}{3} \right)^{n-1} \]

\[ = \quad [?] \quad \boxed{\infty} \]

3. Determine the limit as \( n \) approaches infinity for the given sequence \( v_n \):

\[ v_n = 6n - 3 \]

\[ = \quad [?] \quad \boxed{4} \]

4. Determine the limit as \( n \) approaches infinity for the given sequence \( w_n \):

\[ w_n = 4 \]

\[ = \quad [?] \quad \boxed{\frac{1}{3}} \]

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### Description of Symbols and Limits

- The first equation \( q_n \) is a rational function where the degrees of the polynomial in the numerator and the polynomial in the denominator are compared to find the limit.
- The second equation \( b_n \) involves an exponential function where the base is less than 1.
- The third equation \( v_n \) is a linear function of \( n \).
- The fourth equation \( w_n \) is a constant sequence.

Each sequence is analyzed as \( n \) approaches infinity to find the limit, demonstrating fundamental concepts in sequence and series calculus.
Transcribed Image Text:Below is the transcription of the provided image, suitable for inclusion on an educational website. --- ### Mathematical Sequence Problems 1. Determine the limit as \( n \) approaches infinity for the given sequence \( q_n \): \[ q_n = \frac{n^2 - 5n + 4}{3n^2 + 5} \] \[ = \quad [?] \quad \boxed{0} \] 2. Determine the limit as \( n \) approaches infinity for the given sequence \( b_n \): \[ b_n = 4 \left( \frac{1}{3} \right)^{n-1} \] \[ = \quad [?] \quad \boxed{\infty} \] 3. Determine the limit as \( n \) approaches infinity for the given sequence \( v_n \): \[ v_n = 6n - 3 \] \[ = \quad [?] \quad \boxed{4} \] 4. Determine the limit as \( n \) approaches infinity for the given sequence \( w_n \): \[ w_n = 4 \] \[ = \quad [?] \quad \boxed{\frac{1}{3}} \] --- ### Description of Symbols and Limits - The first equation \( q_n \) is a rational function where the degrees of the polynomial in the numerator and the polynomial in the denominator are compared to find the limit. - The second equation \( b_n \) involves an exponential function where the base is less than 1. - The third equation \( v_n \) is a linear function of \( n \). - The fourth equation \( w_n \) is a constant sequence. Each sequence is analyzed as \( n \) approaches infinity to find the limit, demonstrating fundamental concepts in sequence and series calculus.
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