Question

$1 \div x - 3 - 2 \div x {?}^{2} - 4x + 3$.

Answer 1

7)
$lim \: x - > \sqrt{2} \: \: \: \: \: \: \frac{ {x}^{2} - 2}{ {x}^{2} + \sqrt{2} x - 4}$
apply L'Hospital Rule , differentiate numerator and denomiator with respect to x=>
lim 2x/2x+√2 => lim 2√2/3√2 = 2/3 .
x-> √2 x-> √2
8)
$lim \: \frac{ {x}^{4} - 9}{ {x}^{2} + 4 \sqrt{3} x - 15}(x - > \sqrt{3} )$
apply L'Hospital Rule, differentiate numerator and denomiator with respect to x =>
$lim \: \frac{4 {x}^{3} }{2x + 4 \sqrt{3}}(x - > \sqrt{3} )$
=> lim 4(3√3)/2√3+4√3 = 12√3\6√3 = 2 .
x-> √3
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