Consider the function f(x) = x2 + 3x for x ∈ ℝ and 0 < x < 4. Prove that limx→2 f(x) = 10.

Question

Consider the function f(x) = x2 + 3x for x ∈ ℝ and 0 < x < 4. Prove that limx→2 f(x) = 10.

Answer 1

In this case, we can plug in 2 into f(x) to show that f(x) = 10.

f(x=2) = (2)² + 3(2) = 4 + 6 = 10.

We can do this since plugging in 2 does not lead to things not existing (i.e. divide by zero, infinity, etc.)