Chapter 11: Q. 44 (page 860)

Evaluate the limits in Exercises 42–45.
$\underset{t \to 1^{-}}{l i m} (\ln t, \frac{e^{t} - 1}{t - 1}, e^{t})$

Short Answer

Expert verified

The evaluation of the limit $\underset{t \to 1^{-}}{l i m} (\ln t, \frac{e^{t} - 1}{t - 1}, e^{t})$ is $(0, e, e)$ .

Step by step solution

Step 1. Given Information.

The function:

$\underset{t \to 1^{-}}{l i m} (\ln t, \frac{e^{t} - 1}{t - 1}, e^{t})$

Step 2. Apply the limits.

By applying the limit and solving,

$\underset{t \to 1^{-}}{l i m} (\ln t, \frac{e^{t} - 1}{t - 1}, e^{t}) = \underset{t \to 1^{-}}{l i m} (\ln t) i + \underset{t \to 1^{-}}{l i m} (\frac{e^{t} - 1}{t - 1}) j + \underset{t \to 1^{-}}{l i m} e^{t} k = (\ln 1) i + e^{1} j + e^{1} k = 0 i + e j + e k = (0, e, e)$

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Evaluate the limits in Exercises 42–45.
$\underset{t \to 1^{-}}{l i m} (\ln t, \frac{e^{t} - 1}{t - 1}, e^{t})$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Apply the limits.

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Evaluate the limits in Exercises 42–45.limt→1-(lnt,et-1t-1,et)

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Apply the limits.

One App. One Place for Learning.

Most popular questions from this chapter

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Mechanics Maths

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Applied Mathematics

Study anywhere. Anytime. Across all devices.

Evaluate the limits in Exercises 42–45.
$\underset{t \to 1^{-}}{l i m} (\ln t, \frac{e^{t} - 1}{t - 1}, e^{t})$