Q: Is $$k(x)$$ continuous at $$x=0$$ based on the graph in #18?

No, because $$\lim\limits_{x \to 0} k(x) \neq k(0).$$

Question 1

Given the piecewise function $$g(x) = \begin{cases} x+2 & 	ext{for } x\u003c2 \ \frac{1}{2}x+1 & 	ext{for } x \geq 2 \end{cases}$$, what is $$\lim\limits_{x 	o 2^-} g(x)$$?

Accepted Answer

$$3$$

Question 2

For the same function $$g(x) as $$above, what is $$\lim\limits_{x 	o 2^+} g(x)$$?

Accepted Answer

$$2.5$$

Question 3

Does $$\lim\limits_{x 	o 2} g(x)$$ exist for the function $$g(x)$$ defined above?

Accepted Answer

No, because the left and right limits are not equal.

Question 4

Given the graph of $$F(x) in$$ #2, what is $$\lim\limits_{x 	o 1} F(x)$$?

Accepted Answer

$$-1$$

Question 5

Given the graph of $$F(x) in$$ #3, what is $$\lim\limits_{x 	o 4} F(x)$$?

Accepted Answer

$$-4$$

Question 6

Suppose $$h(x) is $$graphed as in #6. What is $$\lim\limits_{x 	o 2} h(x)$$?

Accepted Answer

$$8$$

Question 7

Given the graph in #7, what is $$\lim\limits_{x 	o 0} m(x)$$?

Accepted Answer

$$3$$

Question 8

Evaluate $$\lim\limits_{x 	o 4} (6x + 1). $$Choose the correct answer.

Accepted Answer

$$25$$

Question 9

Find $$\lim\limits_{x 	o 5} \frac{x^2$ - 9}{5 - x}.$$

Accepted Answer

$$-8$$

Question 10

Find $$\lim\limits_{x 	o 10} \frac{x^2$ - 100}{x - 10}.$$

Accepted Answer

$$20$$

Question 11

Find $$\lim\limits_{x 	o 5} \frac{x^2$ + 3x - 40}{x^2$ - 25}.$$

Accepted Answer

$$\frac{8}{5}$$

Question 12

Given the function $$g(x) = \begin{cases} x+8 & x \leq 9 \ 5x-30 & x \u003e 9 \end{cases}$$, what is $$\lim\limits_{x 	o 9^-} g(x)$$?

Accepted Answer

$$17$$

Question 13

For the same $$g(x) as $$above, what is $$\lim\limits_{x 	o 9^+} g(x)$$?

Accepted Answer

$$15$$

Question 14

Does $$\lim\limits_{x 	o 9} g(x)$$ exist for the function above?

Accepted Answer

No, because the left and right limits are not equal.

Question 15

Suppose $$k(x) is $$graphed as in #18. What is $$\lim\limits_{x 	o 0} k(x)$$?

Accepted Answer

$$-3$$

Question 16

Is $$k(x)$$ continuous at $$x=0$$ based on the graph in #18?

Accepted Answer

No, because $$\lim\limits_{x 	o 0} k(x) 
eq k(0).$$

Question 17

Given the graph in #16, is the function continuous over the interval $$(-6,6)$$?

Accepted Answer

Yes, the function is continuous over $$(-6,6).$$

Question 18

Given the graph in #17, is the function continuous over the interval $$(-6,6)$$?

Accepted Answer

No, because there is a jump discontinuity.

Question 19

Suppose $$f(x) is $$defined as $$f(x) = \begin{cases} x^2$ & x \u003c 2 \ k+2 & x \geq 2 \end{cases}. $$For what value of $$k is$$ $$f(x)$$ continuous at $$x=2$$?

Accepted Answer

$$4$$

Question 20

A business's profit function is $$P(x) = 6x + 1. $$What is the instantaneous rate of change of profit as $$x$$ approaches $$4$$?

Accepted Answer

$$6$$

Limits and Continuity: Graphical and Numerical Approaches in Business Calculus

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