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In this lesson, we will learn how to evaluate limits at infinity algebraically for polynomial and rational functions.
Q1:
Find l i m π₯ β β 2 6 π₯ π₯ β 6 .
Q2:
Find l i m π₯ β β ο 1 6 π₯ + 8 9 π₯ + 3 .
Q3:
Find l i m π₯ β β 2 3 π₯ + 3 8 π₯ + 9 π₯ + 1 .
Q4:
Find l i m π₯ β β 2 2 οΏ 3 π₯ 8 π₯ + 4 β 7 π₯ ( 2 π₯ + 7 ) ο .
Q5:
Find l i m π₯ β β 2 2 β 3 π₯ β 4 π₯ + 8 .
Q6:
Find l i m π₯ β β 4 3 2 4 3 2 3 π₯ β π₯ β π₯ + 3 π₯ + 2 π₯ β 8 π₯ β π₯ β 5 π₯ β 8 .
Q7:
Find l i m π₯ β β β 2 3 9 β 8 π₯ + 6 π₯ β 2 π₯ .
Q8:
Consider the polynomial π ( π₯ ) = 5 π₯ + 9 π₯ β 2 π₯ β π₯ + 1 1 4 3 2 .
Which of the following is equal to l i m π₯ β β π ( π₯ ) ?
Hence, find l i m π₯ β β π ( π₯ ) .
Q9:
Find l i m π₯ β β 2 3 2 7 π₯ + 8 π₯ + 4 5 π₯ + 3 π₯ .
Q10:
Consider the rational function π ( π₯ ) = 3 π₯ β 8 π₯ 9 β 2 π₯ 2 2 .
Which of the following is equal to l i m π₯ β β β π ( π₯ ) ?
Find l i m π₯ β β β π ( π₯ ) .
Q11:
Find the limit of the sequence whose terms are given by .
Q12:
Consider the sequence ( π ) ο β ο ο² ο§ given by π = 2 π + 3 5 π + 6 π ο ο© οͺ ο¨ .
State the first 5 terms of the sequence. If necessary, round your answers to 3 decimal places.
Find the limit of the sequence, if it exists.
Q13:
Find l i m π₯ β β β 4 β 3 β 2 β 1 β 4 β 3 β 2 β 1 β 2 π₯ + 8 π₯ β π₯ + 9 π₯ β 4 2 π₯ β 6 π₯ + 7 π₯ + 6 π₯ + 3 .
Q14:
Determine l i m π₯ β β 3 2 2 ( β 5 π₯ + 4 ) ( 2 π₯ + 4 ) ( π₯ + 2 ) ( 5 π₯ + 1 ) .
Q15:
Determine l i m π₯ β β 2 2 2 2 οΉ 5 π₯ + 3 ο ( π₯ β 5 ) ( 4 π₯ β 3 π₯ ) , if it exists.
Q16:
Find l i m π₯ β β 2 π₯ ο» β 3 6 π₯ + 3 π₯ + 3 β 3 π₯ ο .
Q17:
Determine l i m π₯ β β 2 2 ο» β 6 4 π₯ + 3 π₯ + 4 β β 4 π₯ + 2 π₯ ο .
Q18:
Find l i m π β β 5 5 5 5 π ο οΌ π + 1 π ο β π ο’ .
Q19:
Find the values of π and π , given that l i m ο β β π ( π₯ ) = β 4 and l i m ο β ο« π ( π₯ ) = 5 , where π ( π₯ ) = β π π₯ β 5 4 π π₯ β π₯ + 4 ο¨ ο¨ .
Q20:
Determine l i m π₯ β β 3 2 3 2 π₯ β π₯ β 9 π₯ + 2 ( β 2 π₯ + 5 ) .
Q21:
Determine l i m π₯ β β 8 π₯ + 7 6 | π₯ | β 2 .
Q22:
Find l i m π₯ β β 2 2 οΎ 4 π₯ β 3 β 6 π₯ + 3 + 8 π₯ β 7 π₯ + 3 β 9 π₯ + 5 π₯ + 5 ο .
Q23:
If π ( π₯ ) is a polynomial function of a fifth degrees, and π ( π₯ ) is a polynomial function of a fourth degrees, find l i m ο β β ο« π ( π₯ ) 4 π₯ π ( π₯ ) .
Q24:
Find l i m π₯ β β 4 4 οΎ 3 π₯ 5 π₯ β 3 + 2 β 6 ο π₯ .
Q25:
Find the values of π and π , given that l i m π₯ β β 5 6 5 4 5 π₯ β 2 π₯ + 3 ( π + 4 ) π₯ + ( 1 β π ) π₯ + 5 π₯ = β .
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