lim _{x rightarrow 1} frac{(2 x-3)(sqrt{x}-1) | vedclass

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(C) We evaluate the limit: $\lim _{x \rightarrow 1} \frac{(2 x-3)(\sqrt{x}-1)}{2 x^2+x-3}$ First,factor the denominator: $2x^2+x-3 = (x-1)(2x+3)$ Subs

Vedclass · Accepted Answer

$\frac{-1}{10}$

Vedclass · Answer

(C) We evaluate the limit: $\lim _{x \rightarrow 1} \frac{(2 x-3)(\sqrt{x}-1)}{2 x^2+x-3}$ First,factor the denominator: $2x^2+x-3 = (x-1)(2x+3)$ Substitute this into the limit: $\lim _{x \rightarrow 1} \frac{(2 x-3)(\sqrt{x}-1)}{(x-1)(2 x+3)}$ Recall that $(x-1) = (\sqrt{x}-1)(\sqrt{x}+1)$,so: $\lim _{x \rightarrow 1} \frac{(2 x-3)(\sqrt{x}-1)}{(\sqrt{x}-1)(\sqrt{x}+1)(2 x+3)}$ Cancel the common term $(\sqrt{x}-1)$: $\lim _{x \rightarrow 1} \frac{2 x-3}{(\sqrt{x}+1)(2 x+3)}$ Now,substitute $x=1$: $\frac{2(1)-3}{(\sqrt{1}+1)(2(1)+3)} = \frac{-1}{(2)(5)} = \frac{-1}{10}$

$\lim _{x \rightarrow 1} \frac{(2 x-3)(\sqrt{x}-1)}{2 x^2+x-3}$

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