3 years ago

Rewrite the expression in the form 9^n (9^3) (9^12)

Mathematics

1 answer:

BartSMP [9]3 years ago

5 0

Answer:

${9}^{15}$

Step-by-step explanation:

$( {9}^{3} ) \times ( {9}^{12} ) = 9 {}^{3 + 12} = {9}^{15} \\$

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Evaluate the limit of tan 4x/ 4tan3x

Brut [27]

Answer:

1/3

Step-by-step explanation:

The ratio is undefined at x=0, so we presume that's where we're interested in the limit. Both numerator and denominator are zero at x=0, so L'Hôpital's rule applies. According to that rule, we replace numerator and denominator with their respective derivatives.

$\displaystyle\lim\limits_{x\to 0}\dfrac{\tan{(4x)}}{4\tan{(3x)}}=\lim\limits_{x\to 0}\dfrac{\tan'{(4x)}}{4\tan'{(3x)}}=\lim\limits_{x\to 0}\dfrac{4\sec{(4x)^2}}{12\sec{(3x)^2}}=\dfrac{4}{12}\\\\\boxed{\lim\limits_{x\to 0}\dfrac{\tan{(4x)}}{4\tan{(3x)}}=\dfrac{1}{3}}$