Question

Use the definition of continuity and the properties of limits to show that the function

Answer 1

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:

$\lim_{x \to a} f(x) = f(a)$

In this question:

$f(x) = x^{2} + 5(x-2)^{7}$

At x = 3.

$\lim_{x \to 3} x^{2} + 5(x-2)^{7} = 3^{2} + 5(3-2)^{7} = 14$

$f(3) = 3^{2} + 5(3-2)^{7} = 14$

Since $\lim_{x \to 3} f(x) = f(3)$, f(x) is continuous at x = 3.