(a) To show f(x) is not differentiable at x=1:

f(x) = { x², if x≥1; x, if x<1 }

Left-hand derivative (LHD) at x=1:

LHD = lim (h->0) [f(1-h) - f(1)] / -h = lim (h->0) [(1-h) - 1²] / -h = lim (h->0) [1-h-1] / -h = lim (h->0) [-h] / -h = 1

Right-hand derivative (RHD) at x=1:

RHD = lim (h->0) [f(1+h) - f(1)] / h = lim (h->0) [(1+h)² - 1²] / h = lim (h->0) [1 + 2h + h² - 1] / h = lim (h->0) [2h + h²] / h = lim (h->0) [2 + h] = 2

Since LHD ≠ RHD, f(x) is not differentiable at x=1.

(b) To find λ if f(x) is continuous at x=0:

f(x) = { (sin²λx)/x², if x≠0; 1, if x=0 }

For f(x) to be continuous at x=0, lim (x->0) f(x) = f(0)

lim (x->0) (sin²λx)/x² = 1

lim (x->0) (sin λx / x)² = 1

lim (x->0) (λ * sin λx / λx)² = 1

λ² * lim (x->0) (sin λx / λx)² = 1

Since lim (x->0) (sin λx / λx) = 1, we have λ² * 1² = 1

λ² = 1

λ = ±1