If f(x)=xsin⁡1x, x≠00, x=0 Then limx→0 f(x) - Infinity Learn by Sri Chaitanya

A
1
B
-1
C
0
D
does not exist

Solution:

We have,

$\begin{array}{l} f (x) = \{\begin{matrix} x \sin (\frac{1}{x}), x \neq 0 \\ 0, x = 0 \end{matrix} \\ lim_{x \to 0^{-}} f (x) = lim_{x \to 0} f (0 - h) = lim_{x \to 0} - h \sin (- \frac{1}{h}) \\ \Rightarrow lim_{x \to 0^{-}} f (x) = lim_{x \to 0} h \sin (\frac{1}{h}) = 0 \end{array}$

Similarly, we obtain $lim_{x \to 0^{+}} f (x) = 0 . Hence, lim_{x \to 0} f (x) = 0$

If $f (x) = \{\begin{cases} x \sin (\frac{1}{x}), x \neq 0 \\ 0, x = 0 \end{cases}$ Then $lim_{x \to 0} f (x)$

Solution:

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