How would I solve the following? (finding limits from graphs)

[sktsasus]

1. [FONT=MathJax_Main]lim[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]→[/FONT][FONT=MathJax_Main]3[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main][[/FONT][FONT=MathJax_Math-italic]f[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Math-italic]g[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]][/FONT]
2. [FONT=MathJax_Main]lim[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]→[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main][[/FONT][FONT=MathJax_Math-italic]f[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]/[/FONT][FONT=MathJax_Math-italic]g[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]][/FONT]
3. [FONT=MathJax_Main]lim[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]→[/FONT][FONT=MathJax_Main]3[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main][[/FONT][FONT=MathJax_Math-italic]f[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Math-italic]g[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]][/FONT]
4. [FONT=MathJax_Math-italic]f[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]/[/FONT][FONT=MathJax_Math-italic]g[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main])[/FONT]
[FONT=MathJax_Main]
The first graph is f(x) and second graph is g(x) What I tried to do for part 1 was pinpoint the y-value for when x was 3. I got 3 for f(x) and 0 for g(x). So I added them up and got 3. But this was an incorrect answer. This led to me not being able to do part 2 and 3. For part 4, I tried to pinpoint the corresponding y-value for x=2 and got undefined for f(x) and it seems to be a 2 for g(x). However neither infinite, does not exist or 3/2 were answers. Any help? Note: The 3- denotes that the limit is from the left side of the 3, not that the (f(x)+g(x)) is negative. The same applies for part 2 and 3.
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[mmm4444bot]

1. lim x→3⁻ [f(x) + g(x)]


2. lim x→2⁺ [f(x)/g(x)]


3. lim x→3⁻ [f(x)*g(x)]


4. f(2)/g(2)


… for part 1 … I got 3 for f(x) and 0 for g(x).

The limit for f(x) is 3, but 0 is not correct, for the limit of g(x), as x approaches 3 from the left. Fix that, and you're good to go for part 3, also.

… [Not getting part 1] led to me not being able to do part 2 …

You don't need anything from part 1, to do part 2. Read the limit statements carefully; pay attention to the direction x is moving (i.e., from the left or from the right). Label more values on the axes, if you need help keeping track of dotted-line locations or coordinates on the graphs.

… For part 4, I tried to pinpoint the corresponding y-value for x=2 and got undefined for f(x) and it seems to be a 2 for g(x).

g(2) = 2 is correct, but f(2) is not undefined; look at the image carefully; there is a point with coordinates (2,y). :cool:

 

[sktsasus]

Thank you for your help. I have managed to solve the questions now.