Evaluate numerator and denominator limit, Mathematics

Assignment Help:

Evaluate following limits.

343_limit6.png

Solution : Let's do the first limit & in this case it sees like we will factor a z3 out of the numerator and denominator both. Remember that we just see at the denominator while determining the largest power of z here. In the numerator there is a larger power of z however we ignore it. We just see at the denominator while doing this! So doing the factoring gives,

1415_limit7.png

While we take the limit we'll have to be a little careful. The first term in the numerator & denominator will both be zero.  Though, the z3 in the numerator will be going to plus infinity in the limit and therefore the limit is,

1775_limit8.png

The final limit is negative since we have a quotient of positive quantity & a negative quantity.

Now, let's take a look at the second limit.  Note as well that the only different in the work is at the final "evaluation" step and therefore we'll pick up the work there.

1760_limit9.png

In this case the z3 in the numerator gives -ve infinity in the limit as we are going to minus infinity & the power is odd. The answer is positive as we have a quotient of two negative numbers.


Related Discussions:- Evaluate numerator and denominator limit

Find out that sets of functions are linearly dependent, Find out if the fol...

Find out if the following sets of functions are linearly dependent or independent.  (a) f (  x ) = 9 cos ( 2 x )    g (  x ) = 2 cos2 (  x ) -  2 sin 2 (  x ) (b) f

Without a calculator give the exact value, without a calculator give the ex...

without a calculator give the exact value of each of the following logarithms. (a) (b) log1000 (c) log 16 16 (d) log 23 1  (e)  Solution (b) log10

Sums and differences of cubes and other odd powers, Sums and Differences of...

Sums and Differences of Cubes (and other odd powers)? You can factor a sum or difference of cubes using the formulas a 3 - b 3 = (a - b )(a 2 + ab + b 2 ) and a 3 + b 3 =

Parallel and perpendicular lines, The last topic that we have to discuss in...

The last topic that we have to discuss in this section is that of parallel & perpendicular lines. Following is a sketch of parallel and perpendicular lines. Suppose that th

What is the probability that the card is a queen, Five cards - the ten, jac...

Five cards - the ten, jack, queen, king and ace, are well shuffled with their face downwards. One card is then picked up at random. (i)  What is the probability that the card is

Ratio and proportion, the sides of triangleare inthe ratio 2;3;4 if the per...

the sides of triangleare inthe ratio 2;3;4 if the perimeter is 72 cm. find its side.

Quadratic equation, find a quadratic equation whose roots are q+1/2 and 2p-...

find a quadratic equation whose roots are q+1/2 and 2p-1 with p+q=1

..percentage, how to express 15/4 into percentage

how to express 15/4 into percentage

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