Question 1

Based on the graph provided, what is $$\displaystyle \lim_{x 	o -1} f(x)$$?

Accepted Answer

$$1$$

Question 2

Which of the following statements is true about $$f(x) at$$ $$x = -1$$ based on the graph?

Accepted Answer

The left-hand and right-hand limits at $$x = -1$$ are equal and $$f(-1) is $$defined.

Question 3

What is the value of $$f(-1)$$ according to the graph?

Accepted Answer

$$1$$

Question 4

Which of the following best describes the behavior of $$f(x) as$$ $$x$$ approaches $$1$$ from the left and right?

Accepted Answer

Both limits approach $$3$$ but $$f(1) is $$not defined.

Question 5

At which $$x-$$value does the graph show a jump discontinuity?

Accepted Answer

$$x = 2$$

Question 6

What is $$\displaystyle \lim_{x 	o 2^-} f(x)$$ based on the graph?

Accepted Answer

$$3$$

Question 7

What is $$\displaystyle \lim_{x 	o 2^+} f(x)$$ based on the graph?

Accepted Answer

$$5$$

Question 8

Which of the following is true about the limit at $$x = 2$$?

Accepted Answer

The left- and right-hand limits are not equal, so the limit does not exist at $$x = 2.$$

Question 9

Suppose $$f(x)$$ models the cost (in thousands of dollars) to produce $$x$$ units of a product. What does $$\displaystyle \lim_{x 	o -1} f(x) = 1$$ mean in this context?

Accepted Answer

As production approaches $$-1$$ units, the cost approaches $1,000.

Question 10

If $$f(x)$$ represents the temperature (in degrees Celsius) at time $$x$$ hours, and $$\displaystyle \lim_{x 	o 1} f(x) = 3$$, what does this tell you about the temperature at $$x = 1$$?

Accepted Answer

As time approaches $$1$$ hour, the temperature approaches $$3$$ degrees Celsius, regardless of the value at $$x = 1.$$

Chapter 2: Limits and The Derivative – Introduction to Limits 2.1

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