3 x 8 = 24
24 + 9 = 33
"the number" = 8
Answer:
I. and II. are correct
Step-by-step explanation:
The line y=0 is a horizontal asymptote in both directions, so ...
![\lim\limits_{x\to -\infty}{f(x)}=\lim\limits_{x\to\infty}{f(x)}=0](https://tex.z-dn.net/?f=%5Clim%5Climits_%7Bx%5Cto%20-%5Cinfty%7D%7Bf%28x%29%7D%3D%5Clim%5Climits_%7Bx%5Cto%5Cinfty%7D%7Bf%28x%29%7D%3D0)
The function value f(0) is 0, so the limit is the same from either direction:
![\lim\limits_{x\to 0^-}{f(x)}=\lim\limits_{x\to 0^+}{f(x)}=0](https://tex.z-dn.net/?f=%5Clim%5Climits_%7Bx%5Cto%200%5E-%7D%7Bf%28x%29%7D%3D%5Clim%5Climits_%7Bx%5Cto%200%5E%2B%7D%7Bf%28x%29%7D%3D0)
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The expression for statement III can be simplified:
![\dfrac{f(x)-\dfrac{1}{2}}{x-1}=\dfrac{\dfrac{x}{1+x^2}-\dfrac{1}{2}}{x-1}=\dfrac{2x-(1+x^2)}{2(1+x^2)(x-1)}=\dfrac{-(x-1)^2}{2(x-1)(x^2+1)}\\\\=\dfrac{1-x}{2(x^2+1)}](https://tex.z-dn.net/?f=%5Cdfrac%7Bf%28x%29-%5Cdfrac%7B1%7D%7B2%7D%7D%7Bx-1%7D%3D%5Cdfrac%7B%5Cdfrac%7Bx%7D%7B1%2Bx%5E2%7D-%5Cdfrac%7B1%7D%7B2%7D%7D%7Bx-1%7D%3D%5Cdfrac%7B2x-%281%2Bx%5E2%29%7D%7B2%281%2Bx%5E2%29%28x-1%29%7D%3D%5Cdfrac%7B-%28x-1%29%5E2%7D%7B2%28x-1%29%28x%5E2%2B1%29%7D%5C%5C%5C%5C%3D%5Cdfrac%7B1-x%7D%7B2%28x%5E2%2B1%29%7D)
The limit of this is 0 from either direction, so the limit does exist at x=1.
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We consider that ...
both statements I. and II. are correct.
Answer:
32°, 58°
Step-by-step explanation:
Let one acute angle measure x.
The other acute angle measures 2x - 6.
The sum of the measures of the acute angles of a right triangle is 90.
x + 2x - 6 = 90
3x - 6 = 90
3x = 96
x = 32
2x - 6 = 2(32) - 6 = 58
Answer: 32°, 58°
Answer:
C
Step-by-step explanation:
Since having 1 and 5 as the most likely result is highly unlikely, the answer being 7 points on both numbers would be unfair resulting in C being the answer.
Answer:
2318
Step-by-step explanation: