F x -e1-x-1-e1-x-1-x- 0-f 0 -1 Is function continuous at x-0-

L.H.L=Lth→ 0e^ 1/h 1/e^ 1/h+1=0 1/0+1= 1 #160; #160; R.H.L=Lth→ 0e^1/h 1/e^1/h+1=Lt1 e^ 1/h/1+e^ 1/h=1/1=1 #160; L.H.L.≠ R.H.L. #160;Hen ...

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Functions

f x =e1/x-1/e...

Question

$f (x) = \frac{e^{1 / x} - 1}{e^{1 / x} + 1}, x \neq 0, f (0) = - 1$ Is function continuous at x=0?

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f (x) = \frac{x (e^{1 / x} - e^{- 1 / x})}{e^{1 / x} + e^{- 1 / x}} x \neq 0

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f (x) = \frac{e^{1 / x^{2}}}{e^{1 / x^{2}} - 1}

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f (x) = \frac{x e^{1 / x}}{1 + e^{1 / x}} + sin (1 / x), f (0) = 0

[.]

f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} [x] (\frac{e^{1 / x} - 1}{e^{1 / x} + 1}), & x < 0 b, & x = 0 [x] (\frac{e^{1 / x} - 1}{e^{1 / x} + 1}) + a, & x > 0 \end{matrix}

f (x)

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a + b

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