Evaluate the following exponentials limit, Mathematics

Assignment Help:

Evaluate following limits.

422_limit15.png

Solution: Let's begin this one off in the similar manner as the first part. Let's take the limit of each piece. This time note that since our limit is going to negative infinity the first three exponentials will actually go to zero (since their exponents go to minus infinity in the limit). The final two exponentials will go towards infinity in the limit (since their exponents go to plus infinity in the limit).

Taking limits gives,

504_limit16.png

Thus, the last two terms are the problem as they once again leave us with an indeterminate form.  We will factor out the "largest" exponent in the last two terms. However "largest" doesn't refer to the bigger of the two numbers (-2 is bigger than -15).  Rather than we're going to utilize "largest" to refer to the exponent i.e. farther away from zero.  By using this definition of "largest" means that we're going to factor out an e-15 x.

Again, remember that to factor out this all we actually are doing is dividing each of the term by e-15 x and then subtracting exponents. Following is the work for the first term as an example,

                                 e10 x /e-15 x = e10 x-( -15 x)= e25 x

As along the first part we can either factor out it of only the "problem" terms (that means the last two terms), or all the terms.  For the practice we'll factor it out of all the terms.  Following is the factoring work for this limit,

776_limit17.png

At last, after taking the limit of the two terms (the first is infinity & the second is a negative, finite number) and recalling the Facts through the Infinite Limit section we see that the limit is,

1622_limit18.png

At last, as you might have been capable to guess from the previous example while dealing with a sum and/or difference of exponentials all we have to do is look at the largest exponent to find out the behavior of the whole expression.  Again, recalling that if the limit is at plus infinity we just see at exponentials along with positive exponents & if we're looking at a limit at minus infinity we just see at exponentials with negative exponents.


Related Discussions:- Evaluate the following exponentials limit

Why is the steepness of a curve partially calculate, Can you explain why is...

Can you explain why is the steepness of a curve partially calculated by the units of measurement?

Describe laws of cosines, Q. Describe Laws of Cosines? The law of cosin...

Q. Describe Laws of Cosines? The law of cosines is used to find the missing piece of a triangle if we are given either 1. Two sides and the included angle (SAS) or  2. All t

Set builder notation, For inequalities we contain a similar notation.  Base...

For inequalities we contain a similar notation.  Based on the complexity of the inequality the solution set might be a single number or it might be a range of numbers. If it is jus

Determine the velocity and position functions of object, Determine if the a...

Determine if the acceleration of an object is given by a → = i → + 2 j → + 6tk → find out the object's velocity and position functions here given that the initial velocity is v

Relations, test is tomorrow, don''t know anything lol, please help

test is tomorrow, don''t know anything lol, please help

Index of summation - sequences and series, Index of summation - Sequences a...

Index of summation - Sequences and Series Here now, in the i is termed as the index of summation or just index for short and note that the letter we employ to represent

Commercial arithmetic, if oranges are bought at the rate of 11 for rupees ...

if oranges are bought at the rate of 11 for rupees 10 and are sold at the rate of 10 for rupees 11, find the profit percent

Geometry, how much congruent sides does a trapezoid have

how much congruent sides does a trapezoid have

Territories never was a venitian possesion, Which of those territories neve...

Which of those territories never was a Venitian possesion? Cyprus Morea Crete Sicily

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