How many solutions are in 6x+30+4x=10(x+3)
2 answers:
First, let's simplify the equation.
- Set up
- Combine like terms
- Apply the Distributive Property to the right hand side of the equation
- Subtract
from both sides of the equation
Since the right and left sides of the equation are equal, we know that there must be an infinite number of solutions. This means that there is an infinite amount of values that we can substitute for for the equation to be true.
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Since g(6)=6, and both functions are continuous, we have:
![\lim_{x \to 6} [3f(x)+f(x)g(x)] = 45\\\\\lim_{x \to 6} [3f(x)+6f(x)] = 45\\\\lim_{x \to 6} [9f(x)] = 45\\\\9\cdot lim_{x \to 6} f(x) = 45\\\\lim_{x \to 6} f(x)=5](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%206%7D%20%5B3f%28x%29%2Bf%28x%29g%28x%29%5D%20%3D%2045%5C%5C%5C%5C%5Clim_%7Bx%20%5Cto%206%7D%20%5B3f%28x%29%2B6f%28x%29%5D%20%3D%2045%5C%5C%5C%5Clim_%7Bx%20%5Cto%206%7D%20%5B9f%28x%29%5D%20%3D%2045%5C%5C%5C%5C9%5Ccdot%20lim_%7Bx%20%5Cto%206%7D%20f%28x%29%20%3D%2045%5C%5C%5C%5Clim_%7Bx%20%5Cto%206%7D%20f%28x%29%3D5)
if a function is continuous at a point c, then
,
that is, in a c ∈ a continuous interval, f(c) and the limit of f as x approaches c are the same.
Thus, since
, f(6) = 5
Answer: 5
if a function is continuous at a point c, then
that is, in a c ∈ a continuous interval, f(c) and the limit of f as x approaches c are the same.
Thus, since
Answer: 5