Assuming the existence of the compound shown that is given trivial name, “Ravana” what would you call it in IUPAC?
Assuming the existence of the compound shown that is given trivial name, “Ravana” what would you call it in IUPAC?
$f(5x) = \frac{{5x}}{{5x + 5}} = \frac{x}{{x + 1}}$
Given, $y = \frac{x}{{x + 5}}$
$\therefore y.x + 5y = x$ Continue reading $y = f(x) = \frac{x}{{x + 5}}$ $f(5x) = g(y)$ $g(y) = ?$
Since f is differentiable at 0 we have,
$\mathop {\lim }\limits_{h \to 0} \frac{{f(0 + h) – f(0)}}{h} = \mathop {\lim }\limits_{h \to 0} \frac{{f(0 – h) – f(0)}}{{ – h}}$
$ \Rightarrow \mathop {\lim }\limits_{h \to 0} \frac{{f(h) – f(0)}}{h} = – \mathop {\lim }\limits_{h \to 0} \frac{{f( – h) – f(0)}}{h}$
Since f is an even function, f(-h) = f(h) Continue reading f'(0) = ? for an even function f that is differentiable at 0
${(3{\cos ^2}x + 2\sin x + 1)_{\max }} = ?$
The given expression = $- 3{\sin ^2}x + 2\sin x + 4$
= – $\left[ {{{(\sqrt 3 \sin x)}^2} – 2.\frac{1}{{\sqrt 3 }}.\sqrt 3 \sin x + \frac{1}{3} – \frac{1}{3}} \right]$ + 4
$ = – \left[ {{{\left( {\sqrt 3 \sin x – \frac{1}{{\sqrt 3 }}} \right)}^2} – \frac{1}{3}} \right] + 4$ Continue reading $3{\cos ^2}x + 2\sin x + 1$