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Slove this maths question? Using step by step step and explain

To solve the given limit problem step by step, let's break it down.

### Problem Statement:
\[
\lim_{{x \to 0}} \frac{x}{{4 - x + 16}}
\]

### Step 1: Simplify the expression
First, simplify the expression inside the limit.

The expression is:
\[
\frac{x}{{4 - x + 16}} = \frac{x}{{20 - x}}
\]

This is because \(4 + 16 = 20\).

### Step 2: Apply the limit
Now, apply the limit as \(x\) approaches 0.

\[
\lim_{{x \to 0}} \frac{x}{{20 - x}}
\]

### Step 3: Substitute the value of \(x\) into the expression
Substitute \(x = 0\) into the simplified expression:

\[
\frac{0}{{20 - 0}} = \frac{0}{20} = 0
\]

### Conclusion:
The value of the limit is \(\boxed{0}\).

Would you like further details or have any questions?

### Related Questions:
1. What happens if the limit was \(\lim_{{x \to 0}} \frac{x}{{4 - x + 1}}\)?
2. How would you solve the limit \(\lim_{{x \to 0}} \frac{x^2}{{4 - x + 16}}\)?
3. What if the expression inside the limit was \(\lim_{{x \to 0}} \frac{x + 1}{{20 - x}}\)?
4. How would the result change if \(x\) approached a different value, like \(x \to 1\)?
5. How do you find limits when the expression is a complex fraction?

### Tip:
Always simplify the expression as much as possible before applying the limit to make the calculations easier.

Learn how to solve the limit problem lim(x -> 0) x / (20 - x) step-by-step with a detailed explanation. This problem involves applying limit theorems and algebraic simplification techniques. Suitable for students in Grades 11-12.

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