((x)^(1/3) + (1/( (√x))))^(15) Find the limit that does not inclued the variable x in the opening of the binomial.


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Question Number 148333 by mathdanisur last updated on 27/Jul/21

${(\sqrt[3]{x} + \frac{1}{\sqrt{x}})}^{15}$ $F i n d t h e l i m i t t h a t d o e s n o t i n c l u e d$ $t h e v a r i a b l e x i n t h e o p e n i n g o f t h e$ $b i n o m i a l .$
	Answered by qaz last updated on 27/Jul/21

	$(\begin{matrix} 15 \\ 6 \end{matrix})$
	Commented by mathdanisur last updated on 27/Jul/21

	$H o w S i r$
	Answered by mindispower last updated on 27/Jul/21

	${(a + b)}^{n} = \underset{k = 0}{\sum^{n}} C_{n}^{k} a^{k} b^{n - k}$ $a = x^{\frac{1}{3}}, x^{- \frac{1}{2}}, n = 15$ $= \underset{k = 0}{\sum^{n}} C_{n}^{k} x^{\frac{k}{3}} x^{- \frac{1}{2} (15 - k)}$ $\Rightarrow \frac{k}{3} - \frac{1}{2} (15 - k) = 0$ $\Rightarrow 2 k - 45 + 3 k = 0$ $k = 9$ $t h e c o n s t a n t e i s C_{9}^{15} = C_{15 - 9}^{15} = C_{6}^{15}$
	Commented by mathdanisur last updated on 27/Jul/21

	$T h a n k y o u S e r, a n s w e r : 9 . ?$
	Commented by qaz last updated on 27/Jul/21
	$(x)^(1/3) +(1/( (√x)))=x^(1/3) +x^(−(1/2)) { (((1/3)a−(1/2)b=0)),((a+b=15)) :} ⇒ { ((a=9)),((b=6)) :} So canstant coefficient is (((15)),(( 6)) ).$
	$\sqrt[3]{x} + \frac{1}{\sqrt{x}} = x^{\frac{1}{3}} + x^{- \frac{1}{2}}$ ${\begin{cases} \frac{1}{3} a - \frac{1}{2} b = 0 \\ a + b = 15 \end{cases}$ $\Rightarrow {\begin{cases} a = 9 \\ b = 6 \end{cases}$ $So canstant coefficient is (\begin{matrix} 15 \\ 6 \end{matrix}) .$
	Commented by mathdanisur last updated on 27/Jul/21

	$T h a n k y o u S i r$
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