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

How to calculate mode, Q. How to calculate Mode? The mode of a data set...

Q. How to calculate Mode? The mode of a data set is the value that is repeated most often in the data set. It has the highest frequency. There can be one, more than one, or n

Optimization, Optimization is required in situations that frequentl...

Optimization is required in situations that frequently arise in finance and other areas. Organizations would like to maximize their profits or minimize thei

Ogive, How many types of ogives?

How many types of ogives?

Continuous uniform distribution, Continuous Uniform Distribution Consid...

Continuous Uniform Distribution Consider the interest earned on a bank deposit. Let X equal the value after the decimal point. (Assume no rounding off to the nearest paise.) Fo

Craig D, i need help in discrete mathematics on sets, relations, and functi...

i need help in discrete mathematics on sets, relations, and functions.

Eqt.., pam bought a new bedroom suit for $2588.she me a down payment of $18...

pam bought a new bedroom suit for $2588.she me a down payment of $188 and paid the remaining amount in 24 equal monthly payments .how much did she pay for each monthly payment.

Converting, I need help converting my project fractions to the number 1.

I need help converting my project fractions to the number 1.

The appropriate resource constraint, Consider a person's decision problem i...

Consider a person's decision problem in trying to decide how many children to have. Although she cares about children and would like to have as many as possible, she knows that chi

???, a deposit of 10,000 was made to an account the year you were born afte...

a deposit of 10,000 was made to an account the year you were born after 12 years the account is worth 16,600 what is the simple interest rate did the account earn?

Index numbers, advantages and disadvantages of index numbers

advantages and disadvantages of index numbers

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