Quick Limit Question (Pictures Included)

[Yawzheek]

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.

 

[Nathanael]

You go from (w+4k)/k to (-k-4k)/k but it should be (-k+4k)/k

 

[Yawzheek]

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!

 

[Mark44]

@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.

 

[Yawzheek]

@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.