Hello,
Use the factoration
a^2 - b^2 = (a - b)(a + b)
Then,
x^2 - 81 = x^2 - 9^2
x^2 - 9^2 = ( x - 9).(x + 9)
Then,
Lim (x^2- 81) /(x+9)
= Lim (x -9)(x+9)/(x+9)
Simplity x + 9
Lim (x -9)
Now replace x = -9
Lim ( -9 -9)
Lim -18 = -18
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The second method without using factorization would be to calculate the limit by the hospital rule.
Lim f(x)/g(x) = lim f(x)'/g(x)'
Where,
f(x)' and g(x)' are the derivates.
Let f(x) = x^2 -81
f(x)' = 2x + 0
f(x)' = 2x
Let g(x) = x +9
g(x)' = 1 + 0
g(x)' = 1
Then the Lim stay:
Lim (x^2 -81)/(x+9) = Lim 2x /1
Now replace x = -9
Lim 2×-9 = Lim -18
= -18
Answer:
a^2+a-6
Step-by-step explanation:
i have attached your answer
A) The variable on the horizontal axis of the graph (the independent variable) is "pounds of rice". That is what the first number in the ordered pair (6, 18) represents.
The variable on the vertical axis of the graph (the dependent variable) is "total cost in dollars". That is what the second number in the ordered pair represents.
(6, 18) represents that the total cost of purchasing 6 lbs of rice is $18.
B) The unit price is found at the point where the independent variable has the value 1. That would be at the point (1, 3), which indicates the unit price is $3 per pound.
C) You would have to buy 4 lbs of rice for the total cost to be $12. There are at least two ways to find the answer.
- Draw a horizontal line on the graph at cost = $12. It intersects the graph at lbs = 4.
- Divide the total cost by the unit price. $12/($3/lb) = 4 lb.
Given the stated equation we know that that quadratic formula has 2 as its degree. This meats it has 2 roots. A linear equation has a degree of 1. A linear equation has 1 root. To know if they intersect, the must have one root in common. To know this, solve the two equation simultaneously. If they result to an answer then they intersect.
