(a) Find ‘a’ and ‘b’ if the function f(x) = a {(sinx/x, -2≤x≤0) (a x 2^x , 0≤x≤1) (b + x, 1<x≤2) is continous on [-2,2]

Question

(a) Find ‘a’ and ‘b’ if the function

f(x) = \((a) \begin{cases} {\frac{sin x}{x}} &-2 ≤ x ≤ 0\\\ a \times 2^x & 0≤x≤1\\ b + x ,& 1<x≤2 \end{cases} \) is continous on [-2,2]

(b) How many of the functions

f(x) = |x|, g(x) = |x|², h(x) = |x|³ are not differentiable at x = 0?

(i) 0

(ii) 1

(iii) 2

(iv) 3

Answer 1

(a) Since f(x) is continuous on [-2, 2]

(b) (ii) 1