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

Find the third vertex of equilateral triangle, If two vertices of an equila...

If two vertices of an equilateral triangle are (0, 0) and (3, 0), find the third vertex. [Ans: 3/2 , 3/√ 3/2  or 3/2, -3√ 3/2] Ans:    OA = OB = AB OA 2 = OB 2 = AB 2

Example of implicit differentiation, Example of Implicit differentiation ...

Example of Implicit differentiation So, now it's time to do our first problem where implicit differentiation is required, unlike the first example where we could actually avoid

Comparing, compare 643,251 633,512 and 633.893 the answer is 633.512 what i...

compare 643,251 633,512 and 633.893 the answer is 633.512 what is the question

Outer automorphism, (a) An unordered pair fm; ng with 1 ≤ m ≠ n ≤ 6 is ca...

(a) An unordered pair fm; ng with 1 ≤ m ≠ n ≤ 6 is called a duad. List the 15 duads. (b) There are 15 ways to partition {1, ......, 6 } into 3 duads, such as { {1; 2}, {3, 4},

In sequence to remain the pole perpendicular to the ground, A cable is atta...

A cable is attached to a pole 24 ft above ground and fastened to a stake 10 ft from the base of the pole. In sequence to remain the pole perpendicular to the ground, how long is th

Kyla, hi i am doing the oaks test do you have somthing that could help me

hi i am doing the oaks test do you have somthing that could help me

Shares and dividend, by purchasing rs.10 shares for rs.40 each mala gets 5%...

by purchasing rs.10 shares for rs.40 each mala gets 5% income on her investment. what rate of dividend is the company paying? what will be the amount of dividend if she buys 120 sh

Multiplication of two matrices, Need assignment help, Explain Multiplicatio...

Need assignment help, Explain Multiplication of two Matrices.

The multiplication algorithm, THE MULTIPLICATION ALGORITHM :  Some Class 3...

THE MULTIPLICATION ALGORITHM :  Some Class 3 children in a nearby school had been taught the standard multiplication. Algorithm, and had even done reasonably well in the tests bas

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