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

Statistics, explain the characteristics of statistics

explain the characteristics of statistics

Solution of rectilinear figures, A tower and a monument stand on a level pl...

A tower and a monument stand on a level plane. the angles of depression on top and bottom of the monument viewed from the top of the tower are 13 degrees and 31 degrees, respective

Convert the points into cartesian and polar coordinates, Convert each of th...

Convert each of the following points into the specified coordinate system.  (a) (-4, 2 Π /3) into Cartesian coordinates. (b) (-1,-1) into polar coordinates.  Solution

Calculus, I need help fast with my calculus work

I need help fast with my calculus work

Decmiels, how do you re name percents to decimal

how do you re name percents to decimal

Recognize the importance of famous numbers, Activity This activity will ...

Activity This activity will help you recognize the importance of some very famous numbers, as well as learn more about approximations. Directions Using the Internet, provi

Solid Mensuration, The two sides of a triangle are 17 cm and 28 cm long, an...

The two sides of a triangle are 17 cm and 28 cm long, and the length of the median drawn to the third side is equal to 19.5 cm. Find the distance from an endpoint of this median to

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