Question

√1+x+x² - 1/x
lim
x→0​

Answer 1

Answer:

sub value of X is 0

to get (root 1-infinity)

so answer is root 1= 1

answer 1

Answer 2

lim x→0 [√(1 + x + x²) - 1] / x

• Rationalizing

lim x→0 [√(1 + x + x²) - 1] / x × [√(1 + x + x²) + 1] / [√(1 + x + x²) + 1]

lim x→0 [√(1 + x + x²)² - 1²] / x [√(1 + x + x²) + 1]

lim x→0 (1 + x + x² - 1) / x [√(1 + x + x²) + 1]

lim x→0 x + x² / x [√(1 + x + x²) + 1]

lim x→0 x(1 + x) / x [√(1 + x + x²) + 1]

lim x→0 (1 + x) / [√(1 + x + x²) + 1]

• lim x→0 , x not eqal to zero

•°• = (1 + 0) / [√(1 + 0 + 0) + 1]

= 1 / √1 + 1

= 1 / 1 + 1

= 1/2

The Answer is 1/2