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

Give the introduction to scientific notation, Give the Introduction to Scie...

Give the Introduction to Scientific Notation? In mathematics, it can be very difficult and time-consuming to do calculations involving very large and very small numbers. This i

Linear functions, Linear functions are of the form: y = a 0 ...

Linear functions are of the form: y = a 0 + a 1 x 1 + a 2 x 2 + ..... + a n x n where a 0 , a 1 , a 2 ..... a n are constants and x 1 , x 2 ..... x n a

Principle of superposition, If y 1 (t) and y 2 (t) are two solutions to a...

If y 1 (t) and y 2 (t) are two solutions to a linear, homogeneous differential equation thus it is y (t ) = c 1 y 1 (t ) + c 2 y 2 (t )   ........................(3) Remem

Determine the relative global error, Consider the differential equation giv...

Consider the differential equation give by y′ = -10(y - sin t) (a) Derive by hand exact solution that satis?es the initial condition y(0) = 1. (b) Numerically obtain the s

Compute the center of mass of the solid, 1) Compute the center of mass of t...

1) Compute the center of mass of the solid of unit density 1 bounded (in spherical coordinates) by p=1 and by φ is greater than or equal 0 and less than or equal pi/4

Graphs of sin x and cos x, Q. Graphs of Sin x and Cos x ? Ans. The...

Q. Graphs of Sin x and Cos x ? Ans. The sine and cosine functions are related to the path that an object might take around a circle. Suppose a dolphin was swimming over

Elimination technique of linear equations, What is the Elimination techniqu...

What is the Elimination technique of Linear Equations?

Permuation and combination, how many words can be formed from letters of wo...

how many words can be formed from letters of word daughter such that each word contain 2vowles and 3consonant

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