Evaluate the following limits :
`Lim_(xto1) (x-1)/(2x^(2)-7x+5)`

Explanation

When x = 1, the expression `(x - 1)/(2x^(2) - 7x + 5)` takes the form `(0)/(0)`
`:.` We try to find the common factor in numerator and denominator
`:. underset(x to 1)(lim) (x - 1)/(2x^(2) - 7x + 5) = underset(x to 1)(lim) (x -1)/((x - 1)(2x - 5)) = underset(x to 1)(lim) (1)/(2x - 5) = (1)/(2(1) - 5) = (1)/(3)`
`:. underset(x to 1)(lim) (x - 1)/(2x^(2) - 7x + 5) = (1)/(3)`