The image you uploaded contains mathematical questions written in Arabic, along with various functions and equations. Let me go through the key equations and summarize the information from the image:

Summary of Extracted Information:

1. Question 1:

   • The function $f(x) = x + 1$.
   • It asks to determine the values of $f(\alpha)$ for specific $\alpha$.

2. Question 2:

   • Function involves $f(x) = x^2 - 2x$.
   • The goal seems to be to determine certain limits related to the function $f(x)$.

3. Question 3:

   • Investigates whether a given function is continuous or differentiable.

4. Question 4:

   • There is a relation with $g(x) = 3x^2 + 7x + 3$ and specific limits to evaluate.

5. Question 5:

   • Deals with another limit and function behavior.

6. Other questions:

   • The remaining text appears to explore deeper function analysis, differentiation, and possibly solving differential equations.

Would you like a detailed solution for any specific question from this set?

Here are five related questions to expand on the content:

1. How do you compute the derivative of a function?
2. What is the process of determining the continuity of a function?
3. How can limits be evaluated at infinity for polynomial functions?
4. How can we test if a function is increasing or decreasing?
5. How do you determine whether a function is injective or surjective?

Tip: When solving limits, always check if you can apply L'Hopital's Rule if the limit results in an indeterminate form like 0/0.