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

Credit and invoice, mr ouma bought two sets of spanners for sh 300per set ...

mr ouma bought two sets of spanners for sh 300per set two machanic vice at sh 1000each three set of screw driver at sh 115 per set and tool box for sh 300

Ravens played 25 home games how many games did they win, The Ravens played ...

The Ravens played 25 home games this year. They had 9 losses and 2 ties. How many games did they win? Eleven games are accounted for along with the losses and ties (9 + 2 = 11)

Geometry Question, Does the Angle-Side Relationship Theorm work for all tri...

Does the Angle-Side Relationship Theorm work for all triangles or just a certain type of triangle? Does is correspond with the orthocenter of a triangle?

Fractions, how can I compare fractions with unlike denominators?

how can I compare fractions with unlike denominators?

Quadratic equation, for what k, q.p. kx2-8x+k can be factored into real lin...

for what k, q.p. kx2-8x+k can be factored into real linear factors. kx2-8x+k

The mean value theorem, The Mean Value Theorem : In this section we will ...

The Mean Value Theorem : In this section we will discuss the Mean Value Theorem.  Before we going through the Mean Value Theorem we have to cover the following theorem. Ro

Answer, #questi0+50x1-60-60x0+10on..

#questi0+50x1-60-60x0+10on..

Find out the different strategies of multiplications, 1. Give some Class 4 ...

1. Give some Class 4 children around you problems like 15 x 6 to do dentally. Interact with them to find out the different strategies they use for doing it, and note these down.

Arclength surprise - mathematics, Suppose a unit circle, and any arc S on t...

Suppose a unit circle, and any arc S on the unit circle in the first quadrant. No matter where S is provided, the area between S and the x-axis plus the covered area between S and

Group automorphism, (a) Find an example of groups G, H, K with K  H and H...

(a) Find an example of groups G, H, K with K  H and H G but K G. (b) A subgroup H of G is characteristic if σ(H) ⊆ H for every group automorphism σ of G. Show that eve

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