A student uses the linear approximation L(x)=x to estimate arctanx near x=0. Find the greatest value r>0 such that the approximation error is guaranteed to be less than 0.005 for all x satisfying ∣x∣≤r.
a) ∣x∣≤0.15
b) ∣x∣≤0.25
c) ∣x∣≤0.17
d) ∣x∣≤0.10