 Q: Domain of a function that’s only defined for irrationals I have a function $$f(x) = \dfrac{1}{x^2} \cdot \sin x$$ Its domain is that of the square root $$\sqrt{x} \text{ where } x \in \mathbb{R}, x \ge 0$$ I’m trying to show that: $$\dfrac{1}{x^2} \cdot \sin x \le 0 \forall x \in \mathbb{R}$$ $$f(x) \le 0 \forall x \in \mathbb{R}$$ However I’m unsure on how to prove this, as no matter what I set up in my calculator, the inequality does not hold. Is the inequality true? A: It is not true. Try writing $x$ in the form $2n\pi+\sin\alpha$ for some natural numbers $n,\alpha$. Then $$\frac{1}{x^2}=\frac{1}{(2n\pi+\sin\alpha)^2}=\frac{1}{\sin^2\alpha}+\frac{2n\pi}{\sin^2\alpha} eq 0.$$ UNPUBLISHED UNITED STATES COURT OF APPEALS FOR THE FOURTH CIRCUIT No. 02-7585 JOHNNY L. HILL, Plaintiff – Appellant, versus RAY MABUS,

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Q: I have a button that when pressed toggles it’s visibility and width, but when I do the same with a textview, the width doesn’t change, why? The textview shrinks but the button doesn’t. I have this code for the textview: private void setTextViewSize(final TextView view, int size){ if(size > 0){ //ViewGroup.LayoutParams viewParam = view.getLayoutParams(); view.requestLayout(); //viewParam.width = size; //viewParam.height = size; view.requestLayout(); view.measure(0,0); view.layout(0,0,size,size); view.requestLayout(); } } This is the code for the button: private void setButtonSize(Button button, int size){ if(size > 0){ Button.LayoutParams params = new LayoutParams(size, size); button.setLayoutParams(params); button.requestLayout(); } } This is the layout code for the textview: