Answer:
a) The limit doesnt exist.
b) The limit exists and its value is 1/10
Step-by-step explanation:
a) We take the highest power (x⁴) as common factor in both the numerator and the denominator.
![\lim_{x \to \infty} \frac{x^4-x^3-3x}{7x^2+9} = \lim_{x \to \infty} \frac{x^4(1-1/x-3/x^3)}{x^4(7/x^2+9/x^4)} = \lim_{x \to \infty} \frac{1-1/x-3/x^3}{7/x^2+9/x^4}](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7Bx%5E4-x%5E3-3x%7D%7B7x%5E2%2B9%7D%20%3D%20%20%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7Bx%5E4%281-1%2Fx-3%2Fx%5E3%29%7D%7Bx%5E4%287%2Fx%5E2%2B9%2Fx%5E4%29%7D%20%3D%20%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B1-1%2Fx-3%2Fx%5E3%7D%7B7%2Fx%5E2%2B9%2Fx%5E4%7D)
The limit of the numerator is 1 (when x goes to infinity) and the limit on the second part is 0. Hence the limit doesnt exist (it goes to infinity).
b) Note that if we multiply √x - 5 by its conjugate of , which is √x + 5, we obtain x - 25, thus
![\lim_{x \to 25} \frac{\sqrt x - 5}{x - 25} = \lim_{x \to 25} \frac{(\sqrt{x} - 5)}{(\sqrt{x} - 5) * (\sqrt{x}+5)} = \lim_{x \to 25} \frac{1}{\sqrt x + 5} = \frac{1}{5+5} = \frac{1}{10}](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%2025%7D%20%5Cfrac%7B%5Csqrt%20x%20-%205%7D%7Bx%20-%2025%7D%20%3D%20%5Clim_%7Bx%20%5Cto%2025%7D%20%5Cfrac%7B%28%5Csqrt%7Bx%7D%20-%205%29%7D%7B%28%5Csqrt%7Bx%7D%20-%205%29%20%2A%20%28%5Csqrt%7Bx%7D%2B5%29%7D%20%3D%20%5Clim_%7Bx%20%5Cto%2025%7D%20%5Cfrac%7B1%7D%7B%5Csqrt%20x%20%2B%205%7D%20%3D%20%5Cfrac%7B1%7D%7B5%2B5%7D%20%3D%20%5Cfrac%7B1%7D%7B10%7D)
Hence, the limit exists and its value is 1/10.
Answer:
They are congruent.
Step-by-step explanation:
The have the same side length, as shown by the marking on the side next to the double marked angle and across from single marked angle. They have the same angle measures located in the same places as well. They are congruent as proven by shape, angle measures, and side length.
Answer:
1/23 hope this helps. have a good day/night
Lets get these into improper fractions.
1*8 + 5 = 8+5 = 13
13/8
1*3 + 2 = 3+2 = 5
5/3
Now divide
13/8 = 1.625
5/3 = 1.6666
1 2/3 is larger