Question

If f: R → R is defined by f(x) = [x - 2] + |x - 5| for x ∈ R, then `lim_{x→2^-} f(x)` is equal to ______ 

विकल्प

• 2

• -1

• 0

• 1

Answer 1

If f: R → R is defined by f(x) = [x - 2] + |x - 5| for x ∈ R, then `lim_{x→2^-} f(x)` is equal to 2.

Explanation:

`lim_{x→2^-} f(x) = lim_{x→2^-} [x - 2] + lim_{x→2^-}|x - 5|`

= `lim_{h → 0}[2 - h - 2] + lim_{h → 0}|2 - h - 5|`

= `lim_{h → 0}[-h] + lim_{h → 0}(-3 - h)`

= `lim_{h → 0} (-1) + lim_{h → 0} (3 + h)`

= -1 + 3 = 2