What-is-the-difference-between-lim-x-2-and-lim-x-2-

Question Number 66285 by Rio Michael last updated on 12/Aug/19

W h a t i s t h e d i f f e r e n c e b e t w e e n

\underset{x \to 2^{-}}{l i m} a n d

\underset{x \to 2^{+}}{l i m}

Answered by MJS last updated on 12/Aug/19

limit from left respectively right side . the

two limits can be different

\lim_{x \to 2^{-}} \frac{1}{x - 2} = - \infty

\lim_{x \to 2^{+}} \frac{1}{x - 2} = + \infty

\lim_{x \to 0^{-}} \sqrt[x]{x^{2}} = + \infty

\lim_{x \to 0^{+}} \sqrt[x]{x^{2}} = 0

Answered by GordonYeeman last updated on 12/Aug/19

t h e l i m i t x \to 2 c o n s i s t s o n t a k i n g

a r b i t r a r i l y c l o s e v a l u e s o f 2 (1.99,

1.9999, 1.999999 \dots) . x \to 2^{+} i s b a s i c a l l y

t h e s a m e b u t t h o s e v a l u e s m u s t b e

g r e a t e r t h a n 2 (2.01, 2.000001, e t c) .

I n t h e c a s e o f x \to 2^{-} t h e y m u s t b e

s m a l l e r

Commented by Rio Michael last updated on 12/Aug/19

t h a n k y o u s i r s