Question

Define the function f : [-1/2, [infinity]) → R by f(x) = √(1 + 2x) for x ∈ [-1/2, [infinity]).

Compute the limit as x tends to (-1/2)+ of f(x). Then find the limit as x tends to -1/2 of f(x).

Answer 1

The limit as x tends to (-1/2)+ of f(x) is 0, and the limit as x tends to -1/2 of f(x) is also 0.

Step-by-step explanation:

To compute the limit as x tends to (-1/2)+ of f(x), we substitute (-1/2) into the function f(x) and evaluate the resulting expression:

f((-1/2)+) = √(1 + 2*(-1/2)) = √(1 - 1) = √0 = 0.

To compute the limit as x tends to -1/2 of f(x), we substitute -1/2 into the function f(x) and evaluate the resulting expression:

f(-1/2) = √(1 + 2*(-1/2)) = √(1 - 1) = √0 = 0.