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A group of individuals contains ten people with blood group O, five with group A and five with group B. Give a... Read More

An athlete conceals two performance enhancing tablets in a bottle containing eight vitamin tablets that are similar in appearance. If three tablets... Read More

Locate the global maximum point on the curve $y=xe^{-x^2}$.

Find the inflexion point on $y=e^{-x^2}$.

Prove that $1 + x < e^x < \frac{1}{1-x}$ for all $x\in(0,1)$.

Prove that $e^a (b-a) < e^b – e^a < e^b(b-a)$ for all $a<b$ in $\mathbb{R}$.

Consider the non-zero real-valued function $exp$ on the reals such that $exp(a+b)=exp(a)exp(b)$ and $exp'(a)=exp(a)$ for all real values of $a$ and $b$.... Read More

Where does the following converge $\int_{1}^{\infty} e^{-\alpha x} dx$?

For what values of $\alpha$ will $\int_1^\infty \! x^{-\alpha} \, \mathrm{d}x$ converge?

Show that $f(x) = x^4 – 3x^2 + 1$ has two positive and two negative roots.