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:
Step-by-step explanation:
4(x+1)²=100
(x+1)²= 5²
(x+1)²- 5² = 0
(x+1-5)(x+1+5) = 0 by identity : a² - b ² = (a - b) (a+b)
(x - 4 ) (x+6) =0
x - 4 = 0 or x+6 = 0
x = 4 or x = - 6
You need to <span>draw the diagram to understand the problem easily. Teh diagram will show the right triangle, acute angle with the base 7º, height is 663 m, and "x" is the base of the triangle.
using the tangent ratio:
tan</span>Θ = opposite / adjacent
<span>
tan7º = 663 m / x
x = 663 m / tan7º
x = 5,399.7 m
change m to km. 1,000 m = 1km
5,399.7m * 1km/1,000 m = 5,399.7 km/1000 = 5.3997 km or 5.4 km
B. 5.4 km </span>
