Let [.] denote the greatest integer function and f(x)=⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩[x](e1/x−1e1/x+1),x<0b,x=0[x](e1/x−1e1/x+1)+a ,x>0. If f(x) is continuous at x=0, then the value of a+b is

Let [.] denote the greatest integer function and f(x)=⎧⎪⎪⎪⎪�

1.	Let [.] denote the greatest integer function and f(x)=⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩[x](e1/x−1e1/x+1),x<0b,x=0[x](e1/x−1e1/x+1)+a ,x>0. If f(x) is continuous at x=0, then the value of a+b is
Answer» Let $[.]$ denote the greatest integer function and $f (x) = ⎧ ⎪⎪⎪⎪⎪⎪⎪⎪⎪ ⎨ ⎪⎪⎪⎪⎪⎪⎪⎪⎪ ⎩ \begin{matrix} [x] (\frac{e^{1 / x} - 1}{e^{1 / x} + 1}), & x < 0 b, & x = 0 [x] (\frac{e^{1 / x} - 1}{e^{1 / x} + 1}) + a, & x > 0 \end{matrix}$ . If $f (x)$ is continuous at $x = 0$ , then the value of $a + b$ is