# Calculus

Topic Beta & Gamma functions Statement of Dirichlet’s Theorem $\int \int \int_{V} x^{l-1} y^{m-1} z^{n-1} dx dy ,dz = \frac { \Gamma {(l)} \Gamma {(m)} \Gamma {(n)} }{ \Gamma{(l+m+n+1)} }$ , where V is the region given by $x \ge 0 y \ge 0 z \ge 0 ## Derivative of x squared is 2x or x ? Where is the fallacy? We all know that the derivative of$x^2$is 2x. But what if someone proves it to be just x? ## Solving Ramanujan’s Puzzling Problem Consider a sequence of functions as follows:-$ f_1 (x) = \sqrt {1+\sqrt {x} }  f_2 (x) = \sqrt{1+ \sqrt {1+2 \sqrt {x} } }  f_3 (x) = \sqrt {1+ \sqrt {1+2 \sqrt {1+3 \sqrt {x} } } } $……and so on to$ f_n

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