Question

lim x tends to 2
(x^4 – 16/x^2-5x+6)​

Answer 1

Solution :

Given Expression,

$\sf \displaystyle \lim_{x \longrightarrow \: 2} \: \: \: \dfrac{ {x}^{4} - 16 }{ {x}^{2} - 5x + 6}$

At 2,the given function is in indeterminable form (0/0 form)

$\displaystyle \lim_{x \longrightarrow \: 2} \sf \dfrac{ {x}^{4} - 16 }{ {x}^{2} - 5x + 6}$

The numerator and denominator can be expressed as :

$\implies\displaystyle \lim_{x \longrightarrow \: 2} \sf \dfrac{(x {}^{2} + 4)(x {}^{2} - 4)}{ {x}^{2} - 2x - 3x + 6 } \\ \\ \implies \: \displaystyle \sf \lim_{x \longrightarrow \: 2} \dfrac{( {x}^{2} + 4)(x + 2)(x - 2) }{(x - 2)(x - 3)} \\ \\ \implies \: \sf \: \dfrac{( {2}^{2} + 4)(2 + 2)}{(2 - 3)} \\ \\ \implies \sf{ - 32}$

Answer 2

Step-by-step explanation: