Questions: If the graphs of the functions f and g are shown in the figures, then the limit as x approaches 1 of (f(x) g(x)) =

If the graphs of the functions f and g are shown in the figures, then the limit as x approaches 1 of (f(x) g(x)) =
Transcript text: If the graphs of the functions $f$ and $g$ are shown in the figures, then $\lim _{x \rightarrow 1}(f(x) \&(x))=$
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Solution

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Solution Steps

Step 1: Find the limit of f(x) as x approaches 1

Looking at the graph of f, as x approaches 1, f(x) approaches 2. So, $\lim_{x \rightarrow 1} f(x) = 2$. Note that f(1) = 1, but we are looking for the limit as x _approaches_ 1.

Step 2: Find the limit of g(x) as x approaches 1

Looking at the graph of g, as x approaches 1, g(x) approaches 3. So, $\lim_{x \rightarrow 1} g(x) = 3$. Note that g(1) = 0, but we are interested in the limit as x approaches 1.

Step 3: Find the limit of the product

The limit of the product of two functions is the product of their limits, provided both limits exist. Therefore, $\lim_{x \rightarrow 1}(f(x)g(x)) = (\lim_{x \rightarrow 1} f(x))(\lim_{x \rightarrow 1} g(x)) = (2)(3) = 6$.

Final Answer

6

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