Even / Odd Functions
The graph of an even function is symmetric about the y-axis. Therefore if we have plotted the graph of for , w […]
もっと読む →Welcome to Math World!
The graph of an even function is symmetric about the y-axis. Therefore if we have plotted the graph of for , w […]
もっと読む →Integration by parts is a formula for transforming the integral of the multiplication of two functions. It may […]
もっと読む →Assume that is a rational function of X. Then, in the case of , the substitution will produce an integral of a […]
もっと読む →Let a>0 and . Then, the inverse function of the exponential function is defined as the logarithmic function […]
もっと読む →If and are nonzero vectors in either or , there is a relationship between their inner product and the angle be […]
もっと読む →Proof \begin{eqnarray*}\mathbf{a}\cdot (\mathbf{b}+\mathbf{c})&=&[a_{1} \ a_{2}\ \cdots\ a_{n}]\begin{ […]
もっと読む →Proof \begin{eqnarray*}&&\mathbf{a}\cdot \mathbf{a}=a_{1}a_{1}+a_{2}a_{2}+ \cdots +a_{n}a_{n}\\&&a […]
もっと読む →The integrals of irrational functions are rarely represented by well-known functions. We can calculate only if […]
もっと読む →Proof By the property of the determinant, we have $$\mathrm{det }(AB)=\mathrm{det }A\ \mathrm{det }B$$ Then we […]
もっと読む →Proof We use the property of the transposed matrix : $$(AB)^{t}=B^{t}A^{t}$$ Then we have \begin{eqnarray*}A^{ […]
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