Question

Determine Whether a Piecewise Function Is Continuous Question Use the definition of continuity to decide if the following function is continuous at x = -3. f(x) = x + 3 if x < -3 -1 if x = -3 -0.5x^2 - 1.0x + 2.5 if x > -3 Select the correct answer below: The function is continuous at x = -3. The function is not continuous at x = -3 because the limit at -3 does not exist. The function is not continuous at x = -3 because the limit at -3 does not equal f(-3).

          Determine Whether a Piecewise Function Is Continuous
Question

Use the definition of continuity to decide if the following function is continuous at x = -3.

f(x) = 
x + 3 if x < -3
-1 if x = -3
-0.5x^2 - 1.0x + 2.5 if x > -3

Select the correct answer below:

The function is continuous at x = -3.
The function is not continuous at x = -3 because the limit at -3 does not exist.
The function is not continuous at x = -3 because the limit at -3 does not equal f(-3).

Determine Whether a Piecewise Function Is Continuous
Question

Use the definition of continuity to decide if the following function is continuous at x = -3.

f(x) =
x + 3 if x < -3
-1 if x = -3
-0.5x^2 - 1.0x + 2.5 if x > -3

Select the correct answer below:

The function is continuous at x = -3.
The function is not continuous at x = -3 because the limit at -3 does not exist.
The function is not continuous at x = -3 because the limit at -3 does not equal f(-3).

Added by Jared D.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

06/14/2023

Step 1

For the left side, we have the function x + 3. As x approaches -3, the limit is: $$\lim_{x \to -3^-} (x + 3) = -3 + 3 = 0$$ For the right side, we have the function 0.5x^2 + 1.0x + 2.5. As x approaches -3, the limit is: $$\lim_{x \to -3^+} (0.5x^2 + 1.0x + Show more…

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Determine Whether a Piecewise Function Is Continuous Question Use the definition of continuity to decide if the following function is continuous at x = -3. f(x) = x + 3 if x < -3 -1 if x = -3 -0.5x^2 - 1.0x + 2.5 if x > -3 Select the correct answer below: The function is continuous at x = -3. The function is not continuous at x = -3 because the limit at -3 does not exist. The function is not continuous at x = -3 because the limit at -3 does not equal f(-3).