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zhuklara [117]
3 years ago
10

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

Mathematics
2 answers:
Mashutka [201]3 years ago
8 0

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.

Andrej [43]3 years ago
4 0

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

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