For a function to be continuous at an x-value, say -17, you need to make sure two things line up:
The limit from the left equals the limit from the right.
This limit equals the functions value.
The left hand limit involves the first piece, f(x) = 20x + 1:
![\begin{aligned} \lim_{x \to -17^{-}} f(x) &= \lim_{x \to -17^{-}} (20x+1)\\[0.5em]&= 20(-17)+1\\[0.5em]&= -339\endaligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%20%5Clim_%7Bx%20%5Cto%20-17%5E%7B-%7D%7D%20f%28x%29%20%26%3D%20%20%5Clim_%7Bx%20%5Cto%20-17%5E%7B-%7D%7D%20%2820x%2B1%29%5C%5C%5B0.5em%5D%26%3D%20%20%2020%28-17%29%2B1%5C%5C%5B0.5em%5D%26%3D%20%20%20-339%5Cendaligned%7D)
The right hand limit invovles the second piece, f(x) = -10x^2:
![\begin{aligned} \lim_{x \to -17^{+}} f(x) &= \lim_{x \to -17^{+}} (-10x^2)\\[0.5em]&= -10\cdot (-17)^2\\[0.5em]&= -2890\endaligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%20%5Clim_%7Bx%20%5Cto%20-17%5E%7B%2B%7D%7D%20f%28x%29%20%26%3D%20%20%5Clim_%7Bx%20%5Cto%20-17%5E%7B%2B%7D%7D%20%28-10x%5E2%29%5C%5C%5B0.5em%5D%26%3D%20%20%20-10%5Ccdot%20%28-17%29%5E2%5C%5C%5B0.5em%5D%26%3D%20%20%20-2890%5Cendaligned%7D)
Since the two one-sided limits don't match, the function is not continuous at x=-17.
Answer:
v=pi252(14)
Step-by-step explanation:
v = 1/3Bh
Divide both sides by h.
v/h = 1/3B
Multiply both sides by 3.
3v/h = B
Answer:
<h2>
The width, x, of this parallelogram is 16 cm.</h2>
Step-by-step explanation:
In #14, the area of the parallelogram is 528 cm².
This area is also the value of the formula A = L·W:
A = 528 cm² = (33 cm)·W
To determine the width, W, of this parallelogram, we perform the following division:
W = (528 cm²) / (33 cm) = 16 cm
The width, x, of this parallelogram is 16 cm.
Answer:
6 + 4x − x² = 10 − (x − 2)²
the turning point : (2 , 10)
Step-by-step explanation:
6 + 4x − x² = − x² + 4x + 6
= − (x² − 4x) + 6
= − (x² − 4x + 4 − 4) + 6
= − [(x − 2)² − 4] + 6
= − (x − 2)² + 4 + 6
= − (x − 2)² + 10
= 10 − (x − 2)²
Then the turning point of y is (2 , 10)
