On the interval

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

On the interval

I = [-2, 2]

, if the function

f(x) = \begin{cases} (x+1)e^{-\left(\frac{1}{|x|} + \frac{1}{x}\right)}, & x \neq 0, \\ 0, & x = 0 \end{cases}

then which of the following hold good? (1)

f(x)

is continuous for all values of

x \in I

(2)

f(x)

is continuous for

x \in I - \{0\}

(3)

f(x)

assumes all intermediate values from

f(-2)

f(2)

(4)

f(x)

has a maximum value equal to

3/e