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Question
Evaluate: `lim_(x->1) ((2x - 3)(sqrtx - 1))/(2x^2 + x - 3)`
Solution
`lim_(x->1) ((2x - 3)(sqrtx - 1))/(2x^2 + x - 3)`
`= lim_(x->1) ((2x - 3)(sqrtx - 1))/((2x + 3)(x - 1))` ..`- 6 {(3/2 = 2x + 3),((-2)/2 = x - 1):}`
`= lim_(x->1) ((2x - 3)(sqrtx - 1))/((2x + 3)(sqrtx - 1)(sqrtx + 1))` ...[∵ a2 - b2 = (a + b)(a - b)]
`= lim_(x->1) (2x - 3)/((2x + 3)(sqrtx + 1))`
`= (2(1) - 3)/([2(1) + 3][sqrt1 + 1])`
`= (-1)/((5)(2))`
`= (-1)/10`
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