Yes, because each input value corresponds to exactly one output value.Yes, because the outputs increase as the inputs increase.No, because the graph is not continuous.No, because the curve indicates that the rate of change is not constant.
0 it has no simplest form
Answer:
So sorry , but the pic isn't very seen well
Answer: The ratio is 2.39, which means that the larger acute angle is 2.39 times the smaller acute angle.
Step-by-step explanation:
I suppose that the "legs" of a triangle rectangle are the cathati.
if L is the length of the shorter leg, 2*L is the length of the longest leg.
Now you can remember the relation:
Tan(a) = (opposite cathetus)/(adjacent cathetus)
Then there is one acute angle calculated as:
Tan(θ) = (shorter leg)/(longer leg)
Tan(φ) = (longer leg)/(shorter leg)
And we want to find the ratio between the measure of the larger acute angle and the smaller acute angle.
Then we need to find θ and φ.
Tan(θ) = L/(2*L)
Tan(θ) = 1/2
θ = Atan(1/2) = 26.57°
Tan(φ) = (2*L)/L
Tan(φ) = 2
φ = Atan(2) = 63.43°
Then the ratio between the larger acute angle and the smaller acute angle is:
R = (63.43°)/(26.57°) = 2.39
This means that the larger acute angle is 2.39 times the smaller acute angle.
If f(x) has an inverse on [a, b], then integrating by parts (take u = f(x) and dv = dx), we can show
Let 
. Compute the inverse:
![f\left(f^{-1}(x)\right) = \sqrt{1 + f^{-1}(x)^3} = x \implies f^{-1}(x) = \sqrt[3]{x^2-1}](https://tex.z-dn.net/?f=f%5Cleft%28f%5E%7B-1%7D%28x%29%5Cright%29%20%3D%20%5Csqrt%7B1%20%2B%20f%5E%7B-1%7D%28x%29%5E3%7D%20%3D%20x%20%5Cimplies%20f%5E%7B-1%7D%28x%29%20%3D%20%5Csqrt%5B3%5D%7Bx%5E2-1%7D)
and we immediately notice that ![f^{-1}(x+1)=\sqrt[3]{x^2+2x}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%2B1%29%3D%5Csqrt%5B3%5D%7Bx%5E2%2B2x%7D)
.
So, we can write the given integral as
Splitting up terms and replacing 
in the first integral, we get
