Question

Use the definition of continuity to determine whether f is continuous at a. f(x) = 5x+5 a = -5 Question

Answer 1

Answer:

f is continuous at a = -5.

Step-by-step explanation:

We have given a function.

f(x)  = 5x+5

We have to check continuity of function at a  = -5.

From definition of continuity,

If f is continuous at x = a

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

Putting x  = a = -5 in given function ,we have

f(-5) = 5(-5)+5 = -25+5

f(-5) = -20

$\lim_{x\to-5} f(x) =5(-5)+5$

$\lim_{x \to-5}f(x) = -20$

Hence, $\lim_{x \to-5} f(x)= f(-5)$

f is continuous at a = -5.

Answer 2

ANSWER

$lim_{x \to - 5}(f(x)) = f( - 5)$

EXPLANATION

If f(x) is continuous at

$x = a$

Then,

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

The given function is

$f(x) = 5x + 5$

$f( - 5) = 5( - 5) + 5$

$f( - 5) = - 25 + 5 = - 20$

$lim_{x \to - 5}(f(x)) = 5( - 5) + 5$

$lim_{x \to - 5}(f(x)) = - 20$

Since,

$lim_{x \to - 5}(f(x)) = f( - 5)$

The function is continuous at

$x = - 5$