If $\lim_{x \to 1} \dfrac{x^3 + ax^2 + bx + c}{x^2 - 2x + 1} = 2026$ then the value of $a - c$ is...

If the function $f(x) = \left(\dfrac{5x - 8}{8 - 3x}\right)^{\frac{3}{2x - 4}}$, for $x \neq 2$ is continuous at $x = 2$, then the value of $f(2)$ is...

If the function $f(x) = \dfrac{2\sqrt{2} - (\cos x + \sin x)^3}{1 - \sin 2x}$ is continuous at $x = \dfrac{\pi}{4}$, then the value of $f\left(\dfrac{\pi}{4}\right)$ is ...

The value of $\lim\limits_{x \to 0}\left(\dfrac{8}{x^8}\right)\left[1 - \cos\dfrac{x^2}{2} - \cos\dfrac{x^2}{4} + \cos\dfrac{x^2}{2}\cdot\cos\dfrac{x^2}{4}\right]$ is equal to ...