The value of the expansion $$\mathop {Lim}\limits_{x \to 0} \left[ {{{\sin \left( x \right)} \over {{e^x}X}}} \right]\,\,$$ is

For the function $$\,\,f\left( {x,y} \right) = {x^2} - {y^2}\,\,$$ defined on $${R^2},$$ the point $$(0,0)$$ is

What is the value of $$\mathop {Lim}\limits_{x \to \pi /4} {{\cos x - \sin x} \over {x - \pi /4}}\,\,$$

Given
$$y = \int\limits_1^{{x^2}} {\cos t\,\,\,dt,} $$ $${\,\,\,}$$ then $${{dy} \over {dx}} = \_\_\_\_\_.$$