Answer
2 and 4
I think
Hope this help!
Given:
is continuous,
.
To find:
The value of
and
.
Solution:
If a function f(x) is continuous at
, then
![\lim_{x\to c^-}f(x)=f(c)=\lim_{x\to c^+}f(x)](https://tex.z-dn.net/?f=%5Clim_%7Bx%5Cto%20c%5E-%7Df%28x%29%3Df%28c%29%3D%5Clim_%7Bx%5Cto%20c%5E%2B%7Df%28x%29)
It is given that the function
is continuous. It means it is continuous for each value and the left-hand and right-hand limits are equal to the value of the function.
The function is continuous for 6. So,
![\lim_{x\to 6^-}f(x)=f(6)=\lim_{x\to 6^+}f(x)](https://tex.z-dn.net/?f=%5Clim_%7Bx%5Cto%206%5E-%7Df%28x%29%3Df%286%29%3D%5Clim_%7Bx%5Cto%206%5E%2B%7Df%28x%29)
![\lim_{x\to 6^+}f(x)=f(6)](https://tex.z-dn.net/?f=%5Clim_%7Bx%5Cto%206%5E%2B%7Df%28x%29%3Df%286%29)
![\lim_{x\to 6^+}f(x)=-2](https://tex.z-dn.net/?f=%5Clim_%7Bx%5Cto%206%5E%2B%7Df%28x%29%3D-2)
The function is continuous for -2. So,
![\lim_{x\to -2^-}f(x)=f(-2)=\lim_{x\to -2^+}f(x)](https://tex.z-dn.net/?f=%5Clim_%7Bx%5Cto%20-2%5E-%7Df%28x%29%3Df%28-2%29%3D%5Clim_%7Bx%5Cto%20-2%5E%2B%7Df%28x%29)
![\lim_{x\to -2^-}f(x)=f(-2)](https://tex.z-dn.net/?f=%5Clim_%7Bx%5Cto%20-2%5E-%7Df%28x%29%3Df%28-2%29)
![\lim_{x\to -2^-}f(x)=3](https://tex.z-dn.net/?f=%5Clim_%7Bx%5Cto%20-2%5E-%7Df%28x%29%3D3)
Therefore,
and
.
Answer:
4^-2=1/16
Step-by-step explanation:
When we are multiplying exponents and the bases are the same, we add the exponents
4^6 * 4^-8
4^(6+-8)
4^-2
1/16
9 times 4 is $36 which is the price of the belt
$36 + $9 = 45
$45 + $ 10 = 55 so
<u>Keith had $55 dollars before he bought the shirt and the belt
</u>