Quick Limit Question (Pictures Included)

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In summary, the speaker is seeking clarification on a calculus problem they encountered while studying recreationally. They provide a photo of their attempt and explain their thought process. Another user points out their mistake and the speaker realizes their error. The use of negative signs in their solution was incorrect and they thank the user for their help. The speaker apologizes for not using the required homework template in their post.
  • #1
Yawzheek
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Hey all!

I'm just going back through an old calculus book I have, and while attempting one of the odd numbered problems (because I can check my answers, obviously) I came across a problem and I'm not entirely sure if I've made a serious mistake and completely goofed, or if my book is incorrect. It wouldn't be the first time, and it was a book my physics instructor gave me, and is an instructors first version several years old, but I wanted to check it with you guys. I've included a photo with my attempt. Hopefully it's clear enough to read - the limit is w as it approaches -k.

Also, I've included it in precalculus, since it's a topic often covered in the final chapters of precalculus text, or at least was in my old precalc text, and I've read the template. Trust that you're not helping me in any actual course - this is purely recreational studying, and I have made an attempt to solve it, as you'll see.
 

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  • #2
You go from (w+4k)/k to (-k-4k)/k but it should be (-k+4k)/k
 
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  • #3
Nathanael said:
You go from (w+4k)/k to (-k-4k)/k but it should be (-k+4k)/k

Oh dear God, Nathanael, I think I see what I did now, thank you! Unbelievable! I'm such an idiot...

(w+4k)/w ---> (-k+4k)/-k ---> 3k/-k = -3

I replaced the k in the second term of the numerator with w, and then replaced THAT with -k. I guess it would have been correct, had the equation been (w+4w)/k , but it wasn't, and for WHATEVER reason I arbitrarily attached a negative to the initial k.

Thanks man! Appreciate it!
 
  • #4
@Yawzheek, I notice that you didn't use the homework template. In future posts, please don't delete it, as its use is required in homework posts.
 
  • #5
Mark44 said:
@Yawzheek, I notice that you didn't use the homework template. In future posts, please don't delete it, as its use is required in homework posts.

My apologies, sir. I deleted it because I assumed the photograph, coupled with my attempt to solve the question and explanation would be sufficient.

Again, I'm very sorry for that.
 

Related to Quick Limit Question (Pictures Included)

What is a Quick Limit Question?

A Quick Limit Question is a type of math problem that involves finding the value of a limit using a variety of techniques and strategies. It is often used to test a student's understanding of calculus concepts.

What types of problems are typically included in a Quick Limit Question?

Quick Limit Questions often involve evaluating limits of functions, finding limits at infinity, and using properties of limits such as the squeeze theorem and L'Hopital's rule. They can also involve determining continuity and differentiability of functions at specific points.

How can I approach solving a Quick Limit Question?

First, you should try to simplify the given function by factoring, cancelling, or using algebraic manipulations. Then, you can try to evaluate the limit using direct substitution or other techniques such as finding a common denominator. If these methods do not work, you can also try using graphs, tables, or conceptual reasoning to determine the limit.

What are some common mistakes to avoid when solving a Quick Limit Question?

Some common mistakes include forgetting to check for removable discontinuities, misapplying L'Hopital's rule, and incorrectly using the properties of limits. It is important to carefully read the question and understand the given function before attempting to evaluate the limit.

How can solving Quick Limit Questions improve my understanding of calculus?

Solving Quick Limit Questions requires a deep understanding of calculus concepts such as continuity, differentiability, and properties of limits. By practicing these types of problems, you can improve your problem-solving skills and strengthen your understanding of these fundamental concepts, which are essential for success in calculus and other higher-level math courses.

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