#### niyazikeklk

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Please use "English" for communication at this forum.

Hint: How would you prove that a function is continuous at a given point?

Please show us

Please follow the rules of posting in this forum, as enunciated at:

Please share your work/thoughts about this problem.

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a) \(\displaystyle \lim_{x\to a^+} f(x)\) exists

b) \(\displaystyle \lim_{x\to a^-} f(x)\) exists

c) \(\displaystyle \lim_{x\to a^+} f(x)= \lim_{x\to a^-} f(x)\).

So what are \(\displaystyle \lim_{x\to a^+} f(x)= \lim_{x\to 0} 0\) and \(\displaystyle \lim_{x\to a^-} f(x)= \lim_{x\to 0} (x^2)^a sin^b(x^2)\)?

(It helps to know that \(\displaystyle \lim_{x\to 0}\frac{sin(x)}{x}= 1\).)

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Prof, what you stated above via a-c only shows that the limit at x=a exists. To show continuity at x= a I am sure that you know that you also need to have d) \(\displaystyle \lim_{x\to a} f(x)= f(a)\)

a) \(\displaystyle \lim_{x\to a^+} f(x)\) exists

b) \(\displaystyle \lim_{x\to a^-} f(x)\) exists

c) \(\displaystyle \lim_{x\to a^+} f(x)= \lim_{x\to a^-} f(x)\).

So what are \(\displaystyle \lim_{x\to a^+} f(x)= \lim_{x\to 0} 0\) and \(\displaystyle \lim_{x\to a^-} f(x)= \lim_{x\to 0} (x^2)^a sin^b(x^2)\)?

(It helps to know that \(\displaystyle \lim_{x\to 0}\frac{sin(x)}{x}= 1\).)

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Yes, the last line should have beenProf, what you stated above via a-c only shows that the limit at x=a exists. To show continuity at x= a I am sure that you know that you also need to have d) \(\displaystyle \lim_{x\to a} f(x)= f(a)\)

"\(\displaystyle \lim_{x\to a^-} f(x)= \lim_{x\to a^+} f(x)= f(a)\).