Question

Let a, b ∈ R, b ≠ 0, Define a function

\(f(x) = \begin{cases} a\,sin\cfrac{\pi}{2}(x-1), & for\,x\leq\,0\\ \cfrac{tan\,2x-sin\,2x}{bx^3}, & for\,x>0. \end{cases}\)

If f is continuous at x = 0, then 10 – ab is equal to _____.

Answer 1

\(f(x) = \begin{cases} a\,sin\cfrac{\pi}{2}(x-1), & for\,x\leq\,0\\ \cfrac{tan\,2x-sin\,2x}{bx^3}, & for\,x>0. \end{cases}\)

For continuity at '0'