The families of curves represented by the solution of the equation

$${{dy} \over {dx}} = - {\left( {{x \over y}} \right)^n}$$

for n = –1 and n = 1 respectively, are

Let $$f\left( {x,y} \right) = {{a{x^2} + b{y^2}} \over {xy}}$$, where $$a$$ and $$b$$ are constants. If $${{\partial f} \over {\partial x}} = {{\partial f} \over {\partial y}}$$ at x = 1 and y = 2, then the relation between $$a$$ and $$b$$ is

Taylor series expansion of $$f\left( x \right) = \int\limits_0^x {{e^{ - \left( {{{{t^2}} \over 2}} \right)}}} dt$$ around 𝑥 = 0 has the form

f(x) = $${a_0} + {a_1}x + {a_2}{x^2} + ...$$

The coefficient $${a_2}$$ (correct to two decimal places) is equal to _______.

Given the following statements about a function $$f:R \to R,$$ select the right option:
$$P:$$ If $$f(x)$$ is continuous at $$x = {x_0},$$ then it is also differentiable at $$x = {x_0},$$
$$Q:$$ If $$f(x)$$ is continuous at $$x = {x_0},$$ then it may not be differentiable at $$x = {x_0},$$
$$R:$$ If $$f(x)$$ is differentiable at $$x = {x_0},$$ then it is also continuous at $$x = {x_0},$$