3.1: Definition of Derivative for Oscillating Limits
Which of the following are continuous function?
[math]B\left(x\right)=x\sin\left(\frac{1}{x}\right)[/math] when [math]x\ne0[/math][br][math]B\left(0\right)=0[/math] when [math]x=0[/math]
[math]C\left(x\right)=x^2\sin\left(\frac{1}{x}\right)[/math] when [math]x\ne0[/math][br][math]C\left(0\right)=0[/math] when [math]x=0[/math]
[math]A\left(x\right)=\sin\left(\frac{1}{x}\right)[/math] when [math]x\ne0[/math][br][math]A\left(0\right)=0[/math] when [math]x=0[/math]
Which of the following are differentiable function?
[math]B\left(x\right)=x\sin\left(\frac{1}{x}\right)[/math] when [math]x\ne0[/math][br][math]B\left(0\right)=0[/math] when [math]x=0[/math]
[math]C\left(x\right)=x^2\sin\left(\frac{1}{x}\right)[/math] when [math]x\ne0[/math][br][math]C\left(0\right)=0[/math] when [math]x=0[/math]
[math]A\left(x\right)=\sin\left(\frac{1}{x}\right)[/math] when [math]x\ne0[/math][br][math]A\left(0\right)=0[/math] when [math]x=0[/math]
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Información: 3.1: Definition of Derivative for Oscillating Limits