Maths-
General
Easy

Question

Lt subscript x not stretchy rightwards arrow 0 end subscript fraction numerator 2 x over denominator tan to the power of negative 1 end exponent space x end fraction

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Hint:

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

The correct answer is:


    limit as x rightwards arrow 0 of open parentheses fraction numerator 2 x over denominator tan to the power of negative 1 end exponent 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 2 over denominator open parentheses begin display style fraction numerator 1 over denominator 1 plus x squared end fraction end style close parentheses end fraction close parentheses
equals limit as x rightwards arrow 0 of open parentheses 2 open parentheses 1 plus x squared close parentheses close parentheses
equals 2 open parentheses 1 plus open parentheses 0 close parentheses squared close parentheses
equals 2

    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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