Maths-
General
Easy

Question

Lt subscript x not stretchy rightwards arrow 0 end subscript space open parentheses fraction numerator sin to the power of negative 1 end exponent space x over denominator x end fraction close parentheses

  1.  
  2.  
  3.  
  4.  

    does not exist  

Hint:

Using L’Hospital’s rule, solve the limits.

The correct answer is:


    limit as x rightwards arrow 0 of space open parentheses fraction numerator sin to the power of negative 1 end exponent space x over denominator x end fraction close parentheses
U sin g space L ’ H o s p i t a l ’ s space r u l e comma
equals limit as x rightwards arrow 0 of open parentheses fraction numerator begin display style fraction numerator 1 over denominator square root of 1 minus x squared end root end fraction end style over denominator 1 end fraction close parentheses
equals open parentheses fraction numerator 1 over denominator square root of 1 minus open parentheses 0 close parentheses squared end root end fraction close parentheses
equals 1

    L’Hospital’s rule is a general method of evaluating indeterminate forms such as 0/0 or ∞/∞. L’Hospital’s Rule tells us that if we have an indeterminate form 0/0 or /∞, all we need to do is differentiate the numerator and differentiate the denominator and then take the limit.

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