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

Trigonometry, Prove: 1/cos2A+sin2A/cos2A=sinA+cosA/cosA-sinA

Prove: 1/cos2A+sin2A/cos2A=sinA+cosA/cosA-sinA

Derivatives, application of derivatives in engg.

application of derivatives in engg.

Measurement, into how many smaller part is each centimeter divided

into how many smaller part is each centimeter divided

Circles, assignment on theorems on circle for class 9

assignment on theorems on circle for class 9

Explain angle theorems, Explain Angle Theorems ? Certain angles and an...

Explain Angle Theorems ? Certain angles and angle pairs have special characteristics: Vertical angles are opposite angles formed by the intersection of two lines. Vertical ang

Show that the vector is in the perfect matching polytope, 1.  Let G = (V,E)...

1.  Let G = (V,E) be a graph for which all nodes have degree 5 and where G is 5-edge is connected. a) Show that the vector x which is indexed by the edges E and for which x e =

Calculus, I need help with my calculus work

I need help with my calculus work

Find out height of the box which will give maximum volume, We contain a pie...

We contain a piece of cardboard i.e. 14 inches by 10 inches & we're going to cut out the corners as illustrates below and fold up the sides to form a box, also illustrated below. F

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