Question

Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Match the resulting values to the corresponding limits.

Answer 1

The correct solution to the limits of x in the tiles can be seen below.

• $\mathbf{ \lim_{x \to 9^+} (\dfrac{|x-9|}{-x^2-34+387}) }$$\mathbf{ = -\dfrac{1}{52} }$

• $\mathbf{ \lim_{x \to 8^-} (\dfrac{8-x}{|-x^2-63x+568|}) }$$\mathbf{=\dfrac{1}{79} }$

• $\mathbf{ \lim_{x \to 7^+} (\dfrac{|-x^2-17x+168| }{x-7}) }$= -31

• $\mathbf{ \lim_{x \to 6^-} (\dfrac{|x-6| }{-x^2-86x+552}) }$$\mathbf{ =\dfrac{1}{98}}$

What are the corresponding limits of x?

The limits of x approaching a given number of a quadratic equation can be determined by knowing the value of x at that given number and substituting the value of x into the quadratic equation.

From the given diagram, we have:

1.

$\mathbf{ \lim_{x \to 9^+} (\dfrac{|x-9|}{-x^2-34+387}) }$

So, x - 9 is positive when x → 9⁺. Therefore, |x -9) = x - 9

$\mathbf{ \lim_{x \to 9^+} (\dfrac{x-9}{-x^2-34+387}) }$

Simplifying the quadratic equation, we have:

$\mathbf{ \lim_{x \to 9^+} (-\dfrac{1}{x+43}) }$

Replacing the value of x = 9

$\mathbf{ = (-\dfrac{1}{9+43}) }$

$\mathbf{ = -\dfrac{1}{52} }$

2.

$\mathbf{ \lim_{x \to 8^-} (\dfrac{8-x}{|-x^2-63x+568|}) }$

• -x²-63x+568 is positive when x → 8⁻.

Thus |-x²-63x+568| = -x²-63x+568

$\mathbf{ \lim_{x \to 8^-} (\dfrac{1}{x+71}) }$

$\mathbf{=\dfrac{1}{8+71} }$

$\mathbf{=\dfrac{1}{79} }$

3.

$\mathbf{ \lim_{x \to 7^+} (\dfrac{|-x^2-17x+168| }{x-7}) }$

• x -7 is positive, therefore |x-7| = x - 7

$\mathbf{ \lim_{x \to 7^+} (\dfrac{-x^2-17x+168 }{x-7}) }$

$\mathbf{ \lim_{x \to 7^+} (-x-24)}$

$\mathbf{ \lim_{x \to 7^+} (-7-24)}$

= -31

4.

$\mathbf{ \lim_{x \to 6^-} (\dfrac{|x-6| }{-x^2-86x+552}) }$

• x-6 is negative when x → 6⁻. Therefore, |x-6| = -x + 6

$\mathbf{ \lim_{x \to 6^-} (\dfrac{-x+6 }{-x^2-86x+552}) }$

$\mathbf{ \lim_{x \to 6^-} (\dfrac{1}{x+92}) }$

$\mathbf{ \lim_{x \to 6^-} (\dfrac{1}{6+92}) }$

$\mathbf{ =\dfrac{1}{98}}$

Learn more about calculating the limits of x here:

brainly.com/question/1444047

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