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Question: The equation of the tangent to the curve y = \(\left\{ \begin{matrix} x^{2}\sin\frac{1}{x}, & x \ne...

The equation of the tangent to the curve

y = {x2sin⁡1x,x≠00,x=0 \left\{ \begin{matrix} x^{2}\sin\frac{1}{x}, & x \neq 0 \\ 0, & x = 0 \end{matrix} \right.\ at the origin is

A

x = 0

B

x = y

C

y = 0

D

None of these

Answer

y = 0

Explanation

Solution

(dydx)(0,0)\left( \frac{dy}{dx} \right)_{(0,0)}=lim⁡h→0\lim _ { h \rightarrow 0 } h2−sin⁡1x−θx−θ\frac{h^{2} - \sin\frac{1}{x} - \theta}{x - \theta}= lim⁡h→0\lim_{h \rightarrow 0}x.sin 1h\frac{1}{h}= 0

Ž EOT ® (y – 0) = 0. (x – 0) Ž y = 0