How to Evaluate lim_{x->0^{+}}(1+sinx)^{\frac{1}{\sqrt{x}}}?

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SUMMARY

The limit evaluation of lim_{x->0^{+}}(1+sinx)^{\frac{1}{\sqrt{x}}} results in the indeterminate form 1^{\infty}. To resolve this, the identity 1+sin(x)=e^{ln(1+sin(x))} is utilized, transforming the expression into a more manageable form for analysis. This approach allows for the application of logarithmic properties to simplify the limit evaluation process effectively.

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nhrock3
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lim_{x->0^{+}}(1+sinx)^{\frac{1}{\sqrt{x}}}



i get here 1^{\infty} form which states that's its some sort of exponent
 
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nhrock3 said:
lim_{x->0^{+}}(1+sinx)^{\frac{1}{\sqrt{x}}}



i get here 1^{\infty} form which states that's its some sort of exponent

Use "[ tex]" with no space in front of the 't' and "[ /tex]" with no space in front of the '/'. Capital letters do not work.

RGV
 
lim_{x->0^{+}}(1+sinx)^{\frac{1}{\sqrt{x}}}

Use the identity 1+sin(x)=e^{ln(1+sin(x))}.

ehild
 

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