Use the given graph to determine the limit, if it exists. A coordinate graph is shown with a horizontal line crossing the y axis at three that ends at the open point 2, 3, a closed point at 2, 1, and another horizontal line starting at the open point 2, -2.

Find limit as x approaches two from the left of f of x. and limit as x approaches two from the right of f of x..

Answer:

First part is 8.

Second part is 9.

Step-by-step explanation:

Lucy wants to plant 16 roses, 24 sunflowers, and 32 lilies in her garden.

She wants to plant only one type of flower in each row, and she wants each row to have the same number of plants.

We will take the greatest common factor of 16, 24 and 32

16 = 2 x 2 x 2 x 2

24 = 2 x 2 x 2 x 3

32 = 2 x 2 x 2 x 2 x 2

Now the greatest common factor is = 2 x 2 x 2 = 8

Therefore, the maximum number of flowers she can plant in each row is 8.

All flowers are =

If she plants the maximum number of flowers in each row and uses all of the flowers, she can plant rows of flowers.

Or we can also find this by :

Totaling these we get = rows.

8 and 9

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 2.1   Adding a whole to a fraction 

Rewrite the whole as a fraction using  4  as the denominator :

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole 

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

 2.2       Adding up the two equivalent fractions 
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 3.1   Subtracting a fraction from a whole 

Rewrite the whole as a fraction using  4  as the denominator :

 4.1     Pull out like factors :

   15x + 12y  =   3 • (5x + 4y) 

 4.2       Adding up the two equivalent fractions 

 5.1     Pull out like factors :

   -7x - 16y  =   -1 • (7x + 16y) 

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

Now, on the left hand side, the  4  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
   -7x-16y  = 0

 6.2     Solve   -7x-16y  = 0 

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK). 

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  -7x-16y  = 0 and calculate its properties

Notice that when x = 0 the value of y is 0/-16 so this line "cuts" the y axis at y=-0.00000

When y = 0 the value of x is 0/-7 Our line therefore "cuts" the x axis at x=-0.00000

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 0.000 and for x=2.000, the value of y is -0.875. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -0.875 - 0.000 = -0.875 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)