Question

If, you give Right answer then I mark you Brilliant Answer...
lim x -> 1 x⁷ - 2x⁵ + 1 / x³ - 3x² + 2​

Answer 1

Here when putting limit then it form 0/0

so

Using L hospital Rule..

This rule state that differencate nominator and denominator....and put the limit so that denominator will not zero.

$\lim_{n \to 1} \frac{ {x}^{7} - 2 {x}^{5} + 1 }{ {x}^{3} - 3 {x}^{2} + 2 } \\ \\ = \lim_{n \to 1} \frac{ \frac{d}{dx} ({x}^{7} - 2 {x}^{5} + 1 )}{ \frac{d}{dx} ( {x}^{3} - 3 {x}^{2} + 2)} \\ \\ = \lim_{n \to 1} \frac{7 {x}^{6} - 10 {x}^{4} }{3 {x}^{2} - 6x } \\ Now \: \: put \: \: the \: \: limit \: \: \\ \\ = \frac{7( {1}^{6}) - 10( {1}^{4}) }{3(1 {}^{2} ) - 6(1)} \\ \\ = \frac{7 - 10}{3 - 6} \\ \\ = \frac{ - 3}{ - 3} \\ = 1 \: \: \: \: \: ans$