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limits (2) questions

5)What is the value of 000^0?Isn't it ∞\infty?

LOL this question is raised after i saw the problem
lim⁡x→0sinx0x\lim_{x\rightarrow0}\frac{sin{x^0}}{x} while putting these value I got sin∞0=∞\frac{sin{\infty}}{0}=\infty
yet,in the book the answer is π180\frac{\pi}{180} ,isn't it?but my answer is infinity,am i wrong somewhere?

6) lim⁡x→a(a−x)tanπx2a\lim_{x\rightarrow a}(a-x)tan{\frac{\pi x}{2a}}
I got its answer as 2aπx\frac{2a}{\pi x} but in book the answer is just 2a which one is correct?

thanks a lot...:yes:
Reply 1
Avatar for qgujxj39
qgujxj39
17
TymfAfterDeath
5)What is the value of 000^0?Isn't it ∞\infty?


No, certainly not. There's no absolute answer, see here for a good discussion.

LOL this question is raised after i saw the problem
lim⁡x→0sinx0x\lim_{x\rightarrow0}\frac{sin{x^0}}{x} while putting these value I got sin∞0=∞\frac{sin{\infty}}{0}=\infty
yet,in the book the answer is π180\frac{\pi}{180} ,isn't it?but my answer is infinity,am i wrong somewhere?


I think it means x degrees rather than x to the power of 0.

6)
Unparseable latex formula:

\lim_{x\rightarrowa}(a-x)tan{\frac{\pi x}{2a}}


I got its answer as 2aπx\frac{2a}{\pi x} but in book the answer is just 2a which one is correct?


I can't see the question properly, what is x tending to?
tommm
No, certainly not. There's no absolute answer, see here for a good discussion.



I think it means x degrees rather than x to the power of 0.



I can't see the question properly, what is x tending to?


thanks i corrected it.:yes:
Reply 3
Avatar for DFranklin
DFranklin
18
TymfAfterDeath
6) lim⁡x→a(a−x)tanπx2a\lim_{x\rightarrow a}(a-x)tan{\frac{\pi x}{2a}}
I got its answer as 2aπx\frac{2a}{\pi x} but in book the answer is just 2a which one is correct?Neither, as far as I can tell. Your answer is certainly wrong - if you take the limit as x->a, then you can't have an x appearing in your answer.
As a side point, lim⁡x→0+x0\displaystyle \lim_{x\to 0^+} x^0 is definitely equal to 1*, regardless of what "0^0" equals. There's a good reason you take limits rather than just evaluating directly. But yes, tommm is right, it's meant to be x degrees. Can you do this question now?


(* though notice that lim⁡x→0+0x=0\displaystyle \lim_{x\to 0^+} 0^x = 0, which is why we call 0^0 indeterminate)
generalebriety
As a side point, lim⁡x→0+x0\displaystyle \lim_{x\to 0^+} x^0 is definitely equal to 1*, regardless of what "0^0" equals. There's a good reason you take limits rather than just evaluating directly. But yes, tommm is right, it's meant to be x degrees. Can you do this question now?


(* though notice that lim⁡x→0+0x=0\displaystyle \lim_{x\to 0^+} 0^x = 0, which is why we call 0^0 indeterminate)


I'm also thinking about that it corresponds now with the answer of book.I got it..:woo:

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