https://file.aiquickdraw.com/mathbot/file/17267734221396yscxkg0.jpg

The image contains a mathematical expression involving limits. Here's the relevant part of the equation:

\[
\lim_{{x \to 7}} \frac{\sqrt{x} - \sqrt{7}}{x - 7}
\]

This is a classic example of an indeterminate limit of the form \(\frac{0}{0}\) as \(x\) approaches 7. To solve this, we can use algebraic techniques like multiplying by the conjugate to simplify the expression.

Would you like me to solve this limit problem for you and explain each step in detail? 

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Here are five follow-up questions to deepen your understanding:

1. How do you apply conjugates to solve indeterminate limits?
2. What other techniques can be used to resolve \(\frac{0}{0}\) indeterminate forms?
3. What role does L'Hopital's rule play in limit problems?
4. How does simplifying complex expressions help in calculating limits?
5. Can you think of other examples where multiplying by the conjugate is useful?

**Tip:** When dealing with limits that give an indeterminate form like \(\frac{0}{0}\), always check if algebraic manipulation or L'Hopital's Rule can help simplify the expression.

lim_{x→7} (sqrt(x) - sqrt(7)) / (x - 7)

Solve the limit lim_{x→7} (sqrt(x) - sqrt(7)) / (x - 7) using algebraic techniques like conjugate multiplication. This detailed guide explains each step of resolving indeterminate forms and explores the use of L'Hopital's Rule. Suitable for advanced high school or university students.

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