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(5,13)
I hope the answer will help you in the solution if you want any question no hesitation
I hope the answer will help you in the solution if you want any question no hesitation
The area bounded by the curve, x-axis and y-axis of the function y = √(x + 3) is 2√3
<h3>How to determine the area bounded by the curve, x-axis and y-axis?</h3>The curve is given as:
y = √(x + 3)
The area bounded by the curve, x-axis and y-axis is when x = 0 and y = 0
When y = 0, we have:
0 = √(x + 3)
This gives
x = -3
So, we set up the following integral
A = ∫ f(x) d(x) (Interval a to b)
This gives
A = ∫ √(x + 3) d(x) (Interval -3 to 0)
When the above is integrated, we have:
A = 1/3 * [2(x + 3)^(3/2)] (Interval -3 to 0)
Expand
A = 1/3 * [2(0 + 3)^3/2 - 2(-3 + 3)^3/2]
This gives
A = 1/3 * 2(3)^3/2
Apply the law of indices
A = 2(3)^1/2
Rewrite as:
A = 2√3 or 3.46
Hence, the area bounded by the curve, x-axis and y-axis of the function y = √(x + 3) is 2√3
Read more about areas at:
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Answer:
see below
Step-by-step explanation:
f(x)= -0.08x(x^2-11x+18)
Factor
f(x)= -0.08x(x-9)(x-2)
Using the zero product property to find the zeros
0= -0.08x(x-2)(x-9)
-0.8x =0 x-2 =0 x-9 =0
x=0 x=2 x=9
Multiply out
f(x) = -0.08 x^3 + 0.88 x^2 - 1.44 x
The highest power is x^3
f(-∞) = -0.08( -∞)^3 = - ( -∞) = ∞
As x goes to -∞ f(x) goes to +∞
f(∞) = -0.08( ∞)^3 = - ( ∞) = -∞
As x goes to ∞ f(x) goes to -∞
