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Math Help - Continous function Question

  1. #1
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    Unhappy Continous function Question

    1. f(x) =(x+1)cotx be continuous at x=0 , then f(0)=?

    I think answer is 0
    answer may be 0,1/e,e or none of these

    I am confused what should be the answer explain me the given answer

    Thanks in advance
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  2. #2
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    Re: Continous function Question

    (x+1)^{\cot x}=e^{\cos x\frac{\ln(1+x)}{\sin x}}. Find the limit of the power and, hence, of the function as x\to0 using either L'Hopital's theorem or Taylor series.
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  3. #3
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    Re: Continous function Question

    yes it is continuous at x=0 the limf(x) = e
    define a SEPARATE function using ln and then find the limit to be equal to 1 ..then limf(x)=e
    MINOAS
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  4. #4
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    Re: Continous function Question

    What is the answer A.0 B.1 C.e D.1/e, also show me the calculation
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  5. #5
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    Re: Continous function Question

    Quote Originally Posted by ssss View Post
    show me the calculation
    No, you show us how you followed the advice in posts #2 and #3.
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  6. #6
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    Re: Continous function Question

    Quote Originally Posted by emakarov View Post
    No, you show us how you followed the advice in posts #2 and #3.
    I donot know how to calculate that's why I am asking
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  7. #7
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    Re: Continous function Question

    Have you seem a single example of finding the limit of  \frac{f(x)}{g(x)} where both f(x) and g(x) tend to 0? (Here f(x) = ln(1 + x) and g(x) = sin(x) from post #2.) If not, then you need to read your textbook or lecture notes. This forum is not intended to teach new subjects, only to give hints about subjects that users already know. If yes, then follow the example you read. Read also about the l'H˘pital's rule, which is the simplest way to find such limits. I prefer the method of expanding f(x) and g(x) into Taylor series, though.
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  8. #8
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    Re: Continous function Question

    Quote Originally Posted by emakarov View Post
    Have you seem a single example of finding the limit of  \frac{f(x)}{g(x)} where both f(x) and g(x) tend to 0? (Here f(x) = ln(1 + x) and g(x) = sin(x) from post #2.) If not, then you need to read your textbook or lecture notes. This forum is not intended to teach new subjects, only to give hints about subjects that users already know. If yes, then follow the example you read. Read also about the l'H˘pital's rule, which is the simplest way to find such limits. I prefer the method of expanding f(x) and g(x) into Taylor series, though.
    Thanks , I have not seen this kind of example , I was not getting idea to solve this , Thanks for giving me right path of L Hospital and Taylor Series
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