Hey there!
No, they aren't equal, although they do come close!
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.
Try multiplying each side of the equation by 3, and then
watch out when the answer jumps off the paper at you.
This is the concept of probability and statistics;
The question requires us to get the conditional probability is given by:
P(A|B)=(P(A∩B))/P(B)
but;
P(A∩B)=3/10
P(B)=4/5
thus;
P(A|B)=(3/10)/(4/5)=3/8
The answer is 3/8
Probability is going to be 8/12 2/3 simplified
