Question

The left hand derivative of f(x) = [x] sin(πx) at

x = k, k is an integer and [.] → greatest integer is :

• A. (–1)^k(k – 1)π
• B. (–1)^k–1(k – 1)π
• C. (–1)^k kπ
• D. (–1)^{k – 1} kπ

Answer 1

Answer: (A)

(–1)^k(k – 1)π

Answer 2

L(f '(k)) = $\lim _ { h \rightarrow 0 }$

= $\lim _ { h \rightarrow 0 }$ $\frac { ( - 1 ) ^ { k - 1 } ( k - 1 ) \sin ( \pi h ) - 0 } { - h }$

= (– 1)^k (k – 1)π