Question

lim x^2- square root x by
x->1 square rootx - 1

Answer 1

❖ Question:-

$\displaystyle\lim\limits_{x \to 1} \sf \dfrac{x^2-\sqrt{x}}{\sqrt{x}-1}$

❖answer:-

➼ $\displaystyle\lim\limits_{x \to 1} \sf \dfrac{x^2-\sqrt{x}}{\sqrt{x}-1}$

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➼ $= \displaystyle\lim\limits_{x \to 1} \sf \dfrac{(x^2-\sqrt{x})(\sqrt{x}+1)}{(\sqrt{x}-1)(\sqrt{x}+1)}$

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➼ $= \displaystyle\lim\limits_{x \to 1} \sf \sqrt{x} + x + x^{3/2}$

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➼ $\sf = \sqrt{1} + 1 + 1^{3/2}$

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➼ $\sf = 1 + 1 + 1 = 3$

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Additional Information:-

➳ some important limits

$\boxed{\begin{minipage}{4.5cm}\displaystyle\circ\sf\:\lim\limits_{x \to 0} \sin x = 0 \\\\ \circ\sf\:\lim\limits_{x \to 0} \cos x = 1 \\\\ \circ\sf\:\lim\limits_{x \to 0} \dfrac{\sin x}{x} = 1 \\\\ \circ\sf\:\lim\limits_{x \to 0} \dfrac{\tan x}{x} = 1 \\\\ \circ\sf\:\lim\limits_{x \to 0} \dfrac{\log(1+x)}{x} = 1 \\\\ \circ\sf\;\lim\limits_{x \to 1} e^{x} = 1 \end{minipage}}$

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see answer at : https://brainly.in/question/31833934