Find (i) `underset(x to 5)(lim 6)`
(ii) `underset(x to 2)(lim x)`
(iii)` underset(x to 3)(lim [x + 2])`
(iv) `underset(x to 2)(lim 4x + 2])`

Explanation

(i) `underset(x to 5)(lim) 6 = 6` `[:' underset(x to 3)(lim) C = C` where C is any real number `]`
(ii) `underset(x to 2)(lim) x = 2` `[:' underset(x to a)(lim) x = a]`
(iii) `underset(x to 3)(lim) [x + 2] - underset(x to 3)(lim) x + underset(x to 3)(lim) 2` `[:' underset(x to oo)(lim) (f(x) + g(x)) = underset(x to a)(lim) f (x) + underset(x to a)(lim) g (x)] = 3 + 2 = 5`
(iv) `underset(x to 2) [4x + 2] = underset(x to 2)(lim) 4x + underset(x to 2)(lim)2` `[:' underset(x to oo)(lim) [f(x) + g(x)] = underset(x to a)(lim) f(x) + underset(x to a)(lim) g(x)]`
`= 4 underset(x to 2)(lim) x + underset(x to 2)(lim) 2` `[:' underset(x to a)(lim) lambda f(x) = lambda underset(x to a)(lim) f(x), "where" lambda "is constant"]`
`= 4 (2) + 2 [:' underset(x to a) x = a]`
= 10