Fundraise on MathsGee
First time here? Checkout the FAQs!
x

*Math Image Search only works best with zoomed in and well cropped math screenshots. Check DEMO

0 like 0 dislike
150 views
Determine $\lim_{x \rightarrow \infty}\dfrac{4x^3+x^2}{x^3+3}$
in Mathematics by Platinum (130,996 points) | 150 views

1 Answer

0 like 0 dislike

 

 

As you can see the answer is in the provided picture. The final step cutoff at the bottom says: (4+0)\(1+0) = 4\1 = 4.

Note that this numbers of steps is not necessary in most cases. It is simply to show the method in painstaking detail.

As you can see, we begin by dividing both numerator and denominator by x^3. This reduces all terms to either constants or to terms with powers of x in the denominator. Limits for both of these kinds of terms are easy to evaluate.

Then the quotient law for limits is used (limit of quotient is equal to quotient of limits)

Then the sum law for limits is used (limit of sum is equal to sum of limits)

Finally, the limits are evaluated.

When it comes to tests most of the time I would suggest simply putting in the dividing step, the expression after the division, then (4+0)\(1+0) = 4\1 = 4 in order to save time. The rest of the steps will almost certainly be considered trivial enough that they do no need to be provided.

 

by Wooden Status (248 points)

Related questions

0 like 0 dislike
1 answer
0 like 0 dislike
1 answer
0 like 0 dislike
1 answer
1 like 0 dislike
0 answers
0 like 0 dislike
0 answers
1 like 0 dislike
0 answers
1 like 0 dislike
1 answer
1 like 0 dislike
1 answer
0 like 0 dislike
1 answer
2 like 0 dislike
1 answer
2 like 0 dislike
1 answer
0 like 0 dislike
1 answer

Join the MathsGee Learning Club where you get study and financial support for success from our community. CONNECT - LEARN - FUNDRAISE


On the MathsGee Learning Club, you can:


1. Ask questions


2. Answer questions


3. Vote on Questions and Answers


4. Start a Fundraiser


5. Tip your favourite community member(s)


6. Create Live Video Tutorials (Paid/Free)


7. Join Live Video Tutorials (Paid/Free)


8. Earn points for participating



Posting on the MathsGee Learning Club


1. Remember the human


2. Behave like you would in real life


3. Look for the original source of content


4. Search for duplicates before posting


5. Read the community's rules




CLUB RULES


1. Answers to questions will be posted immediately after moderation


2. Questions will be queued for posting immediately after moderation


3. Depending on how many posts we receive, you could be waiting up to 24 hours for your post to appear. But, please be patient as posts will appear after they pass our moderation.


MathsGee Android Q&A