6. Show that (a) lim(1/n + 7) = 0; (b) lim(n/n + 2) = 2; (c) lim(n/n + 1) = 0; (d) lim(-1)nn/n2 + 1)

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6. Show that
(a) lim(1/√n + 7) = 0;
(b) lim(√n/n + 2) = 2;
(c) lim(√n/n + 1) = 0;
(d) lim(-1)nn/n2 + 1) = 0:
7.
Let xn := 1/ln(n + 1) for n ∈ N.
(a) Use the definition of limit to show that lim(xn) = 0.
(b) Find a specific value of K(ε) as required in the definition of limit for each of (i) ε = 1/2, and (ii) ε = 1/10.