Suppose we want to approximate the function f(x) = sin(x) on the interval [0, 1] by using polynomial interpolation with xo = 0, 21 = 0.5, and x2 = 1. (a) Let pi(x) be the polynomial that interpolates f(x) at ro and 2₁. (i) Find the error bound at x = 0.3 (i.e., the bound for error f(0.3) - p1 (0.3)). (ii) Find the error bound on the whole interval [0, 0.5]. (iii) Use any method of your choice to find p₁(x) and compare the actual error at x = 0.3 with the error bounds in previous steps.

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