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  • If x+4|y|=6 y, then y as a function of x isOption: 1 continuous at x=0Option: 2 d

If x+4|y|=6 y, then y as a function of x is

Option: 1

continuous at x=0


Option: 2

derivable at x=0


Option: 3

\mathrm{\frac{d y}{d x}=\frac{1}{2}} for all x


Option: 4

none of these.


Answers (1)

best_answer

We have, \mathrm{x+4|y|=6 y}
\mathrm{ \Rightarrow\left\{\begin{array}{l} x-4 y=6 y \text { if } y<0 \\ x+4 y=6 y \text { if } y \geq 0 \end{array}\right. }
\mathrm{ \Rightarrow y= \begin{cases}\frac{1}{2} x, & \text { if } x \geq 0 \\ \frac{1}{10} x, & \text { if } x<0\end{cases}}

\mathrm{ \Rightarrow y=f(x)= \begin{cases}\frac{1}{2} x, & x \geq 0 \\ \frac{1}{10} x, & x<0\end{cases}}

Clearly, y=f(x) is continuous at x=0 but it is not differentiable at x=0.

Posted by

Suraj Bhandari

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