Question

lim x tends to 1 x cube minus 1 by x minus 1​

Answer 1

Answer:

3

Step-by-step explanation:

lim x tends to 1

(x^3-1)/(x-1)

x^3-1=(x-1)(x^2+x+1)

=(x^3-1)/(x-1)=(x^2+x+1)

now put x=1 we get

1+1+1=3

Answer 2

SOLUTION

TO EVALUATE

$\displaystyle \sf \lim_{x \to 1} \: \frac{ {x}^{3} - 1 }{x-1}$

EVALUATION

$\displaystyle \sf \lim_{x \to 1} \: \frac{ {x}^{3} - 1 }{x-1}$

$\displaystyle \sf = \lim_{x \to 1} \: \frac{ {x}^{3} - {1}^{3} }{x-1}$

$\displaystyle \sf = \lim_{x \to 1} \: \frac{ (x - 1)( {x}^{2} + x + 1) }{x-1}$

$\displaystyle \sf = \lim_{x \to 1} \:( {x}^{2} + x + 1)$

$\displaystyle \sf = {1}^{2} + 1+ 1$

$\displaystyle \sf =1 + 1 + 1$

$\displaystyle \sf =3$

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