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  • Choose the correct answer out of 4 options given against each Question 〖lim〗┬(x→1) ((√x-1)(2x-3)/(2x^2+x-3)) is A. 1/10

Choose the correct answer out of 4 options given against each Question

\mathop{\lim }_{x \rightarrow 1} \left( \frac{ \left( \sqrt {x}-1 \right) \left( 2x-3 \right) }{2x^{2}+x-3} \right)  is

A. \frac{1}{10}
B. \frac{-1}{10}
C. 1
D. None of these

Answers (1)

\\ \mathop{\lim }_{x \rightarrow 1} \left( \frac{ \left( \sqrt {x}-1 \right) \left( 2x-3 \right) }{2x^{2}+x-3} \right) \\ \\ =\mathop{\lim }_{x \rightarrow 1} \left( \frac{ \left( \sqrt {x}-1 \right) \left( 2x-3 \right) }{ \left( 2x+3 \right) \left( x-1 \right) } \right) \\ \\ =\mathop{\lim }_{x \rightarrow 1} \left( \frac{ \left( \sqrt {x}-1 \right) \left( 2x-3 \right) }{ \left( 2x+3 \right) \left( \sqrt {x}-1 \right) \left( \sqrt {x}+1 \right) } \right) \\ \\ =\mathop{\lim }_{x \rightarrow 1} \left( \frac{ \left( 2x-3 \right) }{ \left( 2x+3 \right) \left( \sqrt {x}+1 \right) } \right) =-\frac{1}{10} \\ \\

Hence, the answer is option B

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