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Right-

Limit as f(x) approaches 10  from the left =   5(10) - 2 =   48

Limit as f(x) approaches 10 from  the right   =   4 / ( 10 + 5)  =  4 / 15

Don't know the exact number but here's how to go about it

1 =  1,1    =  1 point

2 = 1,2   2,1  = 2 points

3 = 1,3,   3,1  = 2 points

4 =  1,4    4,1     2, 2  =    3 points

......

28 =  1,28  28,1   2,14   14,2   4,7   7,4  =  6 points

29 = 1,29    29,1    =   2 points

You need to fill in the rest from  5 to 27, inclusive

The maximum value of the GCD ==1. Because the two expressions are always "relatively prime" to each other, no matter what the value of n is. Therefore, their GCD will always be== 1.

lim f(x)                                            =      45

x approaches 7 from the left

lim f(x)                                            =      1/3 

x approaches 7 from  the right

The limits are not the same....so..we have a discontinuity as  x approaches 7 from  both  sides

**** CORRECTION ***

Round up if 1.A (A is a digit 0-9) applies where A >= 5.
Round down if 1.B (B is a digit 0-9) applies where B < 5.

 \(\displaystyle \text{Let the area of the triangle ABC be }\; \Delta,\\ \text{then }\; \frac{1}{2}AB.AC.\sin A = \Delta.\\ \text{So, since }\;AF=5AB/6,\; \text{and}\;AE=AC/4,\\ \text{the area of the triangle AFE=}\;\frac{1}{2}.\frac{5}{6}AB.\frac{1}{4}AC. \sin A = \frac{5}{24}\Delta.\)

Over to you.

x = 7

Type: Infinite Discontinuity.

(b)

y = x(x + 4)(x - 2)    | distribute

y = x(x² - 2x + 4x - 8)

y = x(x² + 2x - 8)      | distribute

y = x³ + 2x² - 8x

now use integration

\(\int (x^3+2x^2-8x)dx\)

now do it yourself.

(a)

Because the curve C in Figure 3 crosses the x-axis at points A and B, the solutions of the equation are A and B:

y = x(x + 4)(x - 2)

0 = x(x + 4)(x - 2) ...

now solve for x -> x₁ = 0, x₂ = -4 and x₃ = 2

We already know A or B are not zero,

so A = -4 (because A is negative) and B = 2 (because B is positive).

1 1/2 cents = 1.5 cents 

Round up if 1.A (A is a digit 0-9) applies where A > 4.
Round down if 1.B (B is a digit 0-9) applies where B > 5.

so 1.5 cents ≈ 2 cents, like Guest said.

\(\sqrt{\frac{25}{4}} = \frac{\sqrt{25}}{\sqrt{4}} = {\color{blue}\frac{5}{2} = 2 \frac{1}{2}}\)

!!

1 1/2 cents    is   1.5 cents     rounded is 2 cents .

Line equation     y = mx + b

find slope, m      m =  (y1-y2)/(x1-x2)  = 4/1 = 4

y = 4x + b      sub in either of the points to find b = -7

y = 4x -7       re-arrange to requested form

4x - y = 7

4   11   18   25      not in September

  2   9   16    23   30        Winner !    October 30th

Alternatively,

\(\displaystyle (A-2I)(A-4I)=A^{2}-6A+8I=0,\\ A^{2}+8I=6A,\\ A+8A^{-1}=6I.\)

How would you solve this 3/5 of__=24?

Hello Guest!

That means

\(\frac{3}{5}\cdot x =24\ |\ \cdot \frac{5}{3}\\ x=24\cdot \frac{5}{3}\\ \color{blue}x=40\)

\(3/5\ of\ \underline{40}=24\)

  !

3/5 of x = 24 solve for x

24 : 3/5 = 24/1 : 3/5 = 24/1 * 5/3 = 40.

so x = 40 - 3/5 of 40 = 24.

thank you thank you thank you thank you!! 😃😊

x^1 = x, so another one could be 81^1. 

The area of the segment is 6*pi - 12.

I couldn't attach it, but I think it's still possible to solve without it.

If you need the description, here it is:

It's a circle with center O and B and A are two points on the edge of the circle (B comes before A when clockwise).

What diagram?

thank you!! this really helped!!