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In this lesson, we will learn how to use the definition of e (Euler's number) to evaluate some special limits.

Q1:

Determine l i m π₯ β β π₯ + 3 οΌ 1 + 7 π₯ + 9 ο .

Q2:

Determine l i m π₯ β β β 6 π₯ β 5 οΌ 7 π₯ + 5 7 π₯ + 2 ο .

Q3:

Determine l i m π β β 8 π π₯ οΌ 1 β 2 π ο .

Q4:

Determine l i m π₯ β 0 ( π₯ + 1 ) 1 1 1 0 π₯ .

Q5:

Determine l i m t a n π₯ β 0 3 π₯ οΉ β 4 π₯ + 1 ο c o t 3 .

Q6:

Determine l i m π₯ β β π₯ β 3 οΌ π₯ + 4 π₯ β 4 ο .

Q7:

Determine l i m π₯ β β 5 π₯ οΌ 1 β 7 π₯ ο .

Q8:

Determine l i m π₯ β β π₯ οΌ 3 π₯ β 1 1 3 π₯ + 1 1 ο .

Q9:

Consider the binomial expansion for .

Which of the following expressions is its fourth term?

What is the limit of the th term as tends to infinity?

Hence, write in summation (or sigma) notation a series which is equal to the limit of as tends to infinity.

What is the value of this series?

Q10:

Determine l i m π₯ β β π₯ + 2 οΌ 1 + 6 π₯ + 4 ο .

Q11:

Determine l i m π₯ β β π₯ + 2 οΌ 1 + 5 π₯ + 5 ο .

Q12:

Determine l i m π₯ β β π₯ β 3 οΌ 1 + 7 π₯ β 1 ο .

Q13:

Determine l i m π₯ β β π₯ + 3 οΌ 1 + 9 π₯ + 9 ο .

Q14:

Determine l i m π₯ β β 5 π₯ + 4 οΌ 7 π₯ + 2 7 π₯ β 4 ο .

Q15:

Determine l i m π₯ β β π₯ + 5 οΌ π₯ + 4 π₯ β 9 ο .

Q16:

Determine l i m π₯ β β 2 π₯ β 7 οΌ 2 π₯ + 3 2 π₯ + 1 ο .

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