Question

Find the equation of the tangent to the
curve $y=\{\begin{array}{c}{x}^{2}sin\frac{1}{x},x\ne 0\\ 0,x=0\end{array}$

at the origin.

Answer 1

$y=\{\begin{array}{c}{x}^2\sin \frac{1}{x},x\ne 0\\ 0,x=0\end{array}$

$\frac{dy}{dx}={lim}_{h\to 0}\frac{f\left(0+h\right)-f\left(0\right)}{h}$

$={lim}_{h\to 0}\frac{h^2\sin \frac{1}{h}-0}{h}$

$={lim}_{h\to 0}h\sin \frac{1}{h}$

$=0$

$equationoftangent:$

$y-y_1=m\left(x-x_1\right)$

$y-0=0\left(x-0\right)$

$y=0$

$Hence,solved.$