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

Operation research, discuss the sequencing decision problem for n jobs on t...

discuss the sequencing decision problem for n jobs on two and three machines

What is identities and contradictions, What is Identities and Contradiction...

What is Identities and Contradictions ? Look at this equation: x + 1 = 1 + x It happens to be true always, no matter what the value of x. (Try it out! What if x is 43?)

Explain lobachevskian geometry and riemannian geometry, Explain Lobachevski...

Explain Lobachevskian Geometry and Riemannian Geometry ? Nineteenth century mathematician Nicolai Lobachevsky assumed that the summit angles of a Saccheri quadrilateral are ac

What is a set, A set can define as a precise group of distinct objects. Wel...

A set can define as a precise group of distinct objects. Well-defined group means that there be a principle with the help of which it is probable to tell whether a given object rel

Probablility, #question.find the number of combinations of the letters a, b...

#question.find the number of combinations of the letters a, b, c, and d taken 3 at a time.

Work in volume problems, Work : It is the last application of integr...

Work : It is the last application of integral which we'll be looking at under this course. In this section we'll be looking at the amount of work which is done through a forc

Co-ordinate geometry, CO-ORDINATE GEOMETRY : Mathematics  is  the  tool  s...

CO-ORDINATE GEOMETRY : Mathematics  is  the  tool  specially suited  for  dealing with  abstract concepts  of any  kind  and there  is  no limit  to  its  power  in this  field.

Newtons method , Newton's Method : If x n is an approximation a solution ...

Newton's Method : If x n is an approximation a solution of f ( x ) = 0 and if given by, f ′ ( x n ) ≠ 0 the next approximation is given by

, What is 124 out of 300 in percent

What is 124 out of 300 in percent ?

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