The question in the image is:

Jika $\lim_{x \to 3} f(x) = 5$ dan $\lim_{x \to 3} g(x) = 4$, maka $\lim_{x \to 3} (f(x) + g(x)) = \, ?$

To solve this, we use the limit sum property, which states that:

$\lim_{x \to a} (f(x) + g(x)) = \lim_{x \to a} f(x) + \lim_{x \to a} g(x)$

Applying this property:

$\lim_{x \to 3} (f(x) + g(x)) = \lim_{x \to 3} f(x) + \lim_{x \to 3} g(x)$

Since we know:

• $\lim_{x \to 3} f(x) = 5$
• $\lim_{x \to 3} g(x) = 4$

Substitute these values:

$\lim_{x \to 3} (f(x) + g(x)) = 5 + 4 = 9$

Answer:

$\lim_{x \to 3} (f(x) + g(x)) = 9$

Would you like more details on this solution or have any questions?

Here are five related questions to explore:

1. What is the limit of a product $\lim_{x \to a} (f(x) \cdot g(x))$?
2. How would the result change if $\lim_{x \to 3} f(x) = -5$ instead?
3. What happens if one of the limits does not exist?
4. How is the limit sum property useful in other contexts?
5. Can the limit sum property be applied to complex-valued functions?

Tip: When solving limit problems, look for basic properties like sum, product, and quotient rules, as they simplify the process significantly.