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limits!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

0 votes

 

Limit app to 0(1/x arcsinx - 1/x^2)?

asked Mar 30, 2013 in CALCULUS by andrew Scholar

1 Answer

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italic lim with x rightwards arrow 0 below fraction numerator 1 over denominator x a r c italic sin x minus begin display style 1 over x to the power of 2 end style end fraction

italic lim with x rightwards arrow 0 below fraction numerator x to the power of 2 over denominator x to the power of 2 open parentheses x a r c italic sin x minus begin display style 1 over x to the power of 2 end style close parentheses end fraction                    (Multiply numerator and denominator by x^2)

italic lim with x rightwards arrow 0 below fraction numerator x to the power of 2 over denominator open parentheses x to the power of 3 a r c italic sin x minus begin display style x to the power of 2 over x to the power of 2 end style close parentheses end fraction

italic lim with x rightwards arrow 0 below fraction numerator x to the power of 2 over denominator open parentheses x to the power of 3 a r c italic sin x minus 1 close parentheses end fraction

fraction numerator 0 to the power of 2 over denominator open parentheses 0 to the power of 3 a r c italic sin 0 minus 1 close parentheses end fraction                                   (Substitute x = 0 in the limit function)

fraction numerator 0 over denominator open parentheses 0 open parentheses 0 close parentheses minus 1 close parentheses end fraction                                            (Substitute arcsin0 = 0)

fraction numerator 0 over denominator open parentheses 0 minus 1 close parentheses end fraction

fraction numerator 0 over denominator minus 1 end fraction

0.

answered Apr 2, 2013 by diane Scholar

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