The series $$\,\,\sum\limits_{m = 0}^\alpha {{1 \over {{4^m}}}{{\left( {x - 1} \right)}^{2m}}\,\,\,} $$ converges for

Given $$y = {x^2} + 2x + 10\,\,\,$$ the value of $$\,\,{\left. {{{dy} \over {dx}}} \right|_{x = 1}}\,\,$$ is equal to

$$\,\mathop {Lim}\limits_{x \to 0} {{\sin x} \over x}\,\,\,$$ is

For real $$x,$$ the maximum value of $${{{e^{Sin\,x}}} \over {{e^{Cos\,x}}}}\,\,$$ is