$$f = {a_0}\,{x^n} + {a_1}\,{x^{n - 1}}\,y + - - + \,{a_{n - 1}}\,x\,{y^{n - 1}} + {a_n}\,{y^n}$$
where $$\,\,{a_i}\,\,$$ ($$i=0$$ to $$n$$) are constants then $$x{{\partial f} \over {\partial x}} + y{{\partial f} \over {\partial y}}\,\,\,$$ is

$$\mathop {Lim}\limits_{x \to {\pi \over 4}} \,\,{{Sin\,\,2\left( {x - {\pi \over 4}} \right)} \over {x - {\pi \over 4}}} = \_\_\_\_\_\_.$$

$$\mathop {Lim}\limits_{x \to 0} \,{1 \over {10}}\,\,{{1 - {e^{ - j5x}}} \over {1 - {e^{ - jx}}}} = \_\_\_\_.$$