Category Archives: Math
$\sqrt {7 – \sqrt {7 + \sqrt {7 – \sqrt {7 + …..} } } }$
$f(x) = \int\limits_0^x {{\pi ^t}(t – e)(t – \pi )dt} $
$7f(x) + 5f\left( {\frac{1}{x}} \right) = x + 1$ …
${x^5}({x^3} – {x^2} – x + 1)$ + $x(3{x^3} – 4{x^2} – 2x + 4) – 1 = 0$
$\int\limits_0^\infty {\ln \left( {\frac{{{e^x} + 1}}{{{e^x} – 1}}} \right)dx} $
f(x) + f(y) + f(x)f(y) = 1For all values of $x,y \in R$f'(x) = ?
Putting y = x we have,
$2f(x) + {\left[ {f(x)} \right]^2} = 1$
$2f(x) + {\left[ {f(x)} \right]^2} + 1 = 1 + 1$
${[f(x) + 1]^2} = 2$
$f(x) = – 1 \pm \sqrt 2 $
Since f(x) is a constant function, $f'(x) = 0$.