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Katena32 [7]
3 years ago
13

Find the limit of the function algebraically. limit as x approaches negative nine of quantity x squared minus eighty one divided

by quantity x plus nine.
Mathematics
1 answer:
scoray [572]3 years ago
7 0
Let me express the equation clearly:

lim x→-9  (x²-81)/(x+9)

Initially, we solve this by substituting x=-9 to the equation. 

((-9)²-81)/(-9+9) = 0/0

The term 0/0 is undefined. This means that the solution is not see on the number line because it is imaginary. Other undefined terms are N/0 (where N is any number), 0⁰, 0×∞, ∞-∞, 1^∞ and ∞/∞. One way to solve this is by applying L'Hopitals Rule. This can be done by differentiating the numerator and denominator of the fraction independently. Then, you can already substitute the x=-9.

(2x-0)/(1+0) = 2x = 2(-9) = -18

The other easy way is to substitute x=-8.999 to the original equation. Note that the term x→-9 means that x only approaches to -9. Thus, you substitute a number that is very close to -9. Substituting x=-8.999

((-8.999)²-81)/(-8.999+9) = -18

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a = - 1/64

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A square park with sides 15 meters in length has a diagonal walkway as shown.
Alexxandr [17]

Answer:

The approximate length of the diagonal walkway is 21.21 meters

Step-by-step explanation:

we know that

Applying the Pythagorean Theorem in the square park, find out the the approximate length of the diagonal walkway

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we have

a=15\ m\\b=15\ m

substitute

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