Can someone please explain why marks were taken off in this

Can someone please explain why marks were taken off in this

Postby francisg » Wed Feb 14, 2018 8:32 pm

My teacher said I have to solve all the limits at once, but I don't understand why it is wrong to solve one limit before the other.
test picture.jpg
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Re: Can someone please explain why marks were taken off in t

Postby Guest » Mon Feb 19, 2018 7:42 am

The image is very unclear.
Could you please write which limit you would like to be solved?
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Re: Can someone please explain why marks were taken off in t

Postby HallsofIvy » Sat Jul 25, 2020 9:48 am

Gosh, this is so blasted hard to read! Everyone, if you care at all about people here helping you,type the problems in, do not post unreadable photos of the problem!

I think that the problem you are asking about is to find [tex]\lim_{x\to 0}\frac{sin(5x)}{2x(x- 2)}[/tex]. And you did this by writing it as [tex]\frac{1}{2}\lim_{x\to 0}\frac{sin(5x)}{x}\frac{1}{x-2}= \frac{5}{2}\left(\lim_{x\to 0}\frac{sin(5x)}{5x}\right)\left(\lim_{x\to 0}\frac{1}{x- 2}\right)[/tex].

You can do those two limits separately because "[tex]\lim_{x\to a}f(x)g(x)= \left(\lim_{x\to a}f(x)\right)\left(\lim_{x\to a} g(x)\right)[/tex]" Of course, [tex]\lim_{x\to 0}\frac{1}{x- 2}= \frac{1}{0- 2}= -\frac{1}{2}[tex] and [tex]\lim_{x\to 0}\frac{sin(5x)}{5x}= 1[/tex] so the original limit is (5/2)(-1/2)(1)= -5/4.

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