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

Percentage change, in a sale a clothes shop reduces its prices by 30% a shi...

in a sale a clothes shop reduces its prices by 30% a shirt usually costs £38 how much is it in the sale

Produce list containing m-vectors delta and lambda, The logarithm of the Po...

The logarithm of the Poisson mixture likelihood (3.10) can be calculated with the following R code: sum(log(outer(x,lambda,dpois) %*% delta)), where delta and lambda are m-ve

Find the sides of the two squares, The sum of areas of two squares is 468m ...

The sum of areas of two squares is 468m 2  If the difference of their perimeters is 24cm, find the sides of the two squares. Ans:    Let the side of the larger square be x .

Quadratic Functions, Can you please explain what Quadratic functions are?

Can you please explain what Quadratic functions are?

Example of word problem, Example of Word problem: There is a man who i...

Example of Word problem: There is a man who is 21 years older than his son.  5 years ago he was four times as old as his son. How older are both now? Solution: Step 1

Example of exponential smoothing, Example of Exponential Smoothing ...

Example of Exponential Smoothing By using the previous example and smoothing constant 0.3 generate monthly forecasts Months Sales Forecast

Harmonic mean-arthmetic geometric progression, Harmonic mean It is a m...

Harmonic mean It is a measure of central tendency which is utilized to determine the average increase rates for natural economies. This is defined like the reciprocal of the a

Addition and subtraction, In addition and subtraction we have discussed ...

In addition and subtraction we have discussed 1) Some ways of conveying the meaning of the operations of addition and subtraction to children. 2) The different models o

Shares and dividend, a man in rested rupee 800 is buying rupee 5 shares and...

a man in rested rupee 800 is buying rupee 5 shares and then are selling at premium of rupee 1.15. He sells all the shares.find profit

Measurement of the sampling distribution, Caterer determines that 87% of p...

Caterer determines that 87% of people who sampled the food thought it was delicious. A random sample of 144 out of population of 5000 taken. The 144 are asked to sample the food. I

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