Answers:
The limit as x approaches 3 does not exist (DNE)
The function value f(3) is equal to 5, so f(3) = 5
In short, the answer is choice B
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Explanations:
Let's start with computing the limit. First locate 3 on the x axis. Then move slightly to the left of 3, say to x = 2. Draw a vertical line upward until you hit the function curve. Mark the point on the function curve and then drag that point closer and closer to x = 3. Notice how y is getting loser to y = 3.
Then do the same for the other side of x = 3. Start at x = 4 and move to the left to get to x = 3. Get closer and closer, and you'll notice that y is getting closer to y = 5. These two differing y values tell us that the limit as x approaches 3 does not exist.
Alternatively: The left hand limit (LHL) and right hand limit (RHL) are different, so the overall limit does not exist.
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The function value f(3) is simply 5 because we draw a vertical line through x = 3 and it intersects the function at (3,5). Take note how I'm focusing on the closed circle and not the open circle. The open circle is a gap or hole in the graph.
Note: because the limit at x = 3 and the function value at x = 3 differ, this means we have a discontinuity.
Given that amount of first acid solution = 4 liters
Let concentration of the first acid solution = x
then effective amount of first solution = 4x
Given that amount of second acid solution = 10 liters
Givn that concentration of the second acid solution = 40% = 0.4
then effective amount of second solution = 0.4(10)
Then amount of resulting acid solution = (4+10) liters
Givn that concentration of the resulting acid solution = 30% = 0.3
then effective amount of resulting solution = 0.3(4+10)
Combining all those results gives equation
4x +0.4(10) = 0.3(4+10)
4x +4 = 0.3(14)
4x +4 = 4.2
4x = 0.2
x=0.05
Hence final answer is 0.05 or you can say 5%.
Add the last two equations to eliminate <em>x</em> :
(<em>x</em> - 2<em>y</em> - 3<em>z</em>) + (- <em>x</em> + <em>y</em> + 2<em>z</em>) = 0 + 3
- <em>y</em> - <em>z</em> = 3
<em>y</em> + <em>z</em> = -3
Subtract this from the first equation to eliminate <em>z</em>, then solve for <em>y</em> :
(2<em>y</em> + <em>z</em>) - (<em>y</em> + <em>z</em>) = -8 - (-3)
<em>y</em> = -5
Plug this into the first equation to solve for <em>z</em> :
2(-5) + <em>z</em> = -8
<em>z</em> = 2
Plug both of these into either the second or third equations to solve for <em>x</em> :
<em>x</em> - 2(-5) - 3(2) = 0
<em>x</em> = -4
10m + -0.4 = 9.6
-0.4 + 10m = 9.6
-0.4 + 10m = 9.6
Solving for 'm'Move all terms containing m to the left, all other terms to the right.
-0.4 + 0.4 + 10m = 9.6 + 0.4
Combine like terms: -0.4 + 0.4 = 0.00.0 + 10m = 9.6 + 0.410m = 9.6 + 0.4
Combine like terms: 9.6 + 0.4 = 1010m = 10
Divide each side by '10'.<span>m = 1</span>
