(i) Check the continuity of the function given by f(x) f(x) = ​​{ (x sin (1/x), x ≠ 0)(1,(x = 0))

Question

(i) Check the continuity of the function given by f(x)

f(x) = \(\begin{cases}x sin {\frac{1}{x}} & x ≠ 0\\\ 1 & x = 0 \end{cases} \)

(ii) Verify Mean Value Theorem for the function f(x) = x + \(\frac{1}{x}\) in the interval [1,3].

Answer 1

given ; f(o) = 1. So f (x) is discontinuous at x = 0

⇒ C² = 3

⇒ C = \(\sqrt {3}\) ∈ (1,3)

Hence Mean Value Theorem ¡s verified.