Evaluate limit in l''hospital''s rule form, Mathematics

Assignment Help:

Evaluate the below given limit.

645_limit50.png

Solution

Note as well that we actually do have to do the right-hand limit here. We know that the natural logarithm is just described for positive x and thus it is the only limit that makes any sense.

Now, in the limit, we obtain the indeterminate form (0) (-∞).  L'Hospital's Rule won't apply on products, it works on quotients only.  Though, we can turn it into a fraction if we rewrite things a little.

545_limit51.png

The function is the similar, just rewritten, & now the limit is in the form -∞ /∞ and now we can utilizes L'Hospital's Rule.

904_limit52.png

Now, it is a mess, however it cleans up nicely.

1446_limit53.png

Now let's take a look at the indeterminate forms,

                1∞                00         ∞0

These can all be dealt with in the given way therefore we'll just work one example.


Related Discussions:- Evaluate limit in l''hospital''s rule form

Least common denominator, Let's recall how do to do this with a rapid numbe...

Let's recall how do to do this with a rapid number example.                                                     5/6 - 3/4 In this case we required a common denominator & reme

Parallel and perpendicular lines, The last topic that we have to discuss in...

The last topic that we have to discuss in this section is that of parallel & perpendicular lines. Following is a sketch of parallel and perpendicular lines. Suppose that th

Percentages, how to remember the formulas of this topic

how to remember the formulas of this topic

How to adding rational expressions with common denominators, Adding Rationa...

Adding Rational Expressions with Common Denominators To add or subtract fractions or rational expressions with common denominators, all you do is add or subtract the numerators

Michael has 16 cds how many cds does kathleen have, Michael has 16 CDs. Th...

Michael has 16 CDs. This is four more than twice the amount that Kathleen has. How many CDs does Kathleen have? Let x = the number of CDs Kathleen has. Four more than twice th

Determine the measure of a base angle, The angle calculate of the base angl...

The angle calculate of the base angles of an isosceles triangle are shown by x and the vertex angle is 3x + 10. Determine the measure of a base angle. a. 112° b. 42.5° c.

Largest number of vertices in a graph, a) Specify that a tree has at least ...

a) Specify that a tree has at least 2 vertices of degree 1.                               b) What is the largest number of vertices in a graph with 35 edges if all vertices are

Bottleneck for each product, A company makes 2 products, Product A and Prod...

A company makes 2 products, Product A and Product B. The product characteristics are shown in the following table. Product A B

Radicals, We'll include this section with the definition of the radical.  I...

We'll include this section with the definition of the radical.  If n is a +ve integer that is greater than one and a is a real number then, Where n is termed as the index,

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd