Answer:
Applied the definition and the limit.
They had the same result, so the function is continuous.
Step-by-step explanation:
At function f(x) is continuous at x = a if:
[tex]\lim_{x \to a} f(x) = f(a)[/tex]
In this question:
[tex]f(x) = x^{2} + 5(x-2)^{7}[/tex]
At x = 3.
[tex]\lim_{x \to 3} x^{2} + 5(x-2)^{7} = 3^{2} + 5(3-2)^{7} = 14[/tex]
[tex]f(3) = 3^{2} + 5(3-2)^{7} = 14[/tex]
Since [tex]\lim_{x \to 3} f(x) = f(3)[/tex], f(x) is continuous at x = 3.
