LimitsHard
Question
Let [x] denote the greatest integer less than or equal to x. If f(x) = [x sin πx], then f(x) is :
Options
A.continuous at x = 0
B.continuous in (-1, 0)
C.differentiable at x = 1
D.differentiable in (-1, 1)
Solution
f(x) = [x sin πx]
f(0) = 0
f(0-) =
[-h sin π(-h)] = 0 ; f(0+) = 
[h sin πh] = 0 Here f(0-) = f(0+) = f(0) = 0
So continuous at x = 0
Since graph of f(x) is as shown in the figure
Now all options can be checked from graph.
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