please help ... thanks

[Calvin Teo]

 

[lex]

For the sake of it!

(b)
[MATH] \begin{align}\\ |\sin^2 x - \sin^2 y| & = \frac{1}{2} |\cos 2y - \cos 2x|\\ & =|\sin(x+y)\sin(x-y)|\\ & ≤|x-y| \hspace5ex \text{ since } |\sin u|≤1 \text{ and } |\sin u|≤|u| \end{align}\\ [/MATH]

 

[Cubist]

For the sake of it!

Tut tut, I hope that the following inequality holds:- allotted exam time ≤ 8 days ??

 

[lex]

Tut tut, I hope that the following inequality holds:- allotted exam time ≤ 8 days ??

Venusian days, of course.

 

[pka]

View attachment 27268

If we know that \(|f(x)|\le|x|^{\frac{3}{2}}[\forall x\in(-\infty,\infty)]\), what does that tell us about \(f(0)~?\)
Then is it the case that \(|f(0+h)-f(0)|=|(f(h)|\le|h|^{\frac{3}{2}}~?\)
To finish we need to know how the apply the \(\varepsilon/\delta\) definition of the derivative.