Match each item in List I with its value in List II. List I: (A) number of points where f ( x ) = ∣ sin π x ∣ on [ − 1 , 0 ) , f ( x ) = 1 − { x } on [ 0 , 1 ) , f ( 1 ) = 0 , and f ( x ) = 1 + ⌊ cos

Question

Match each item in List I with its value in List II. List I: (A) number of points where $f (x) = ∣ sin π x ∣$ on $[- 1, 0)$ , $f (x) = 1 - {x}$ on $[0, 1), f (1) = 0$ , and $f (x) = 1 + ⌊ cos (π x /2)⌋$ on $(1, 2]$ is continuous but nondifferentiable; (B) left derivative at 0 of $f (x) = x^{2} e^{1/ x}$ for $x \neq = 0, f (0) = 0$ ; (C) number of points where $g (x) = 1/ (1 + 1/ f (x)^{2})$ is not differentiable, with $f (x) = 1/ (1 + 1/ x)$ ; (D) number of points where the curve $y = sgn (x^{2} - 1)$ has no tangent. List II:

Options:

Answer:

A

Solution:

Direct piecewise checks give: (A) one point; (B) 0; (C) three points (including domain breaks); and (D) two points, at $x = \pm 1$ . Hence A-Q, B-P, C-S, D-R.

TestHub · Accepted Answer

Direct piecewise checks give: (A) one point; (B) 0; (C) three points (including domain breaks); and (D) two points, at x = ± 1 . Hence A-Q, B-P, C-S, D-R.

Mathematics - Continuity - Differentiability Question with Solution | TestHub

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