Evaluate the following limit: `underset( x rarr 1) ( "lim")(x^7-2x^5+1)/(x^3-3x^2+2)`

Explanation

Given,

`(lim)_(x->1)(x^7−2x^5+1)/(x^3−3x^2+2)`

`=(lim)_(x->1)(1^7−2xx1^5+1)/(1^3−3xx1^2+2)`

`=0/0`

thus,

applying L-Hospital Rule,

`(lim)_(x->1)(x^7−2x^5+1)/(x^3−3x^2+2)`

`=(lim)_(x->1)(7x^6−10x^4)/(3x^2−6x)`

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