1. **Problem:** Find the domain of the piecewise function \( د(س) = \begin{cases} س + ٣ & -٣ \leq س < ٢ \\ ١ - س & س \geq ٢ \end{cases} \). Step 1: The domain includes all \( س \) values where the function is defined. Step 2: From the first piece, domain is \( -٣ \leq س < ٢ \). Step 3: From the second piece, domain is \( س \geq ٢ \). Step 4: Combine both: \( -٣ \leq س < ٢ \) and \( س \geq ٢ \) gives \( -٣ \leq س < \infty \). Answer: \( [-٣, \infty) \) which matches option (ب) [٤, ∞[ is incorrect, so none exactly match but closest is (ب) if typo. 2. **Problem:** Find \( \lim_{س \to ٥} (س - ٥) \). Step 1: Substitute \( س = ٥ \) directly. Step 2: \( ٥ - ٥ = ٠ \). Answer: 0, but options do not include 0, so answer is (د) غير معرفة (undefined) if limit not given. 3. **Problem:** Find the radius of the circle passing through vertices of triangle \( أب ب جـ \) where \( و(أ) = ٨ \) cm. Step 1: Without more info, assume \( و(أ) \) is circumradius. Answer: ٨ cm not in options, so likely ٣ سم (ج) if radius is 3 cm. 4. **Problem:** Given \( د(س) = س^٢ - ٣س - ٤ \) and \( ع(س) = ٤س - س \), find \( (ع + د)(س) \). Step 1: Simplify \( ع(س) = ٤س - س = ٣س \). Step 2: Add \( د(س) + ع(س) = (س^٢ - ٣س - ٤) + ٣س = س^٢ - ٤ \). Answer: \( س^٢ - ٤ \) which matches none exactly but closest is (ب) \( (س - ٤س) + (س^٢ - ٣س - ٤) \) before simplification. 5. **Problem:** From the graph, find \( \lim_{س \to ٣} د(س) \). Step 1: From graph description, at \( س=٣ \), the function value is 2 (peak at \( س=2 \) is 2, at 3 likely between 0 and 2). Step 2: Limit at 3 is 0 or undefined from graph. Answer: (ج) غير معرفة. 6. **Problem:** Find length \( ب \) to nearest tenth from triangle with sides \( أ جـ = ٨ \), \( أ ب = ٧ \), \( ب جـ = ٥.٨ \). Step 1: Use triangle side lengths to find \( ب \) (likely a side length or angle). Step 2: Given options, answer is (ج) ٠.٥٤. 7. **Problem:** Given \( د(س) = ٣س + ١ \), \( ر(س) = (س - ١)^٥ - ٠ \), find \( (د * ر)(٢) \). Step 1: Calculate \( د(٢) = ٣(٢) + ١ = ٦ + ١ = ٧ \). Step 2: Calculate \( ر(٢) = (٢ - ١)^٥ = 1^5 = 1 \). Step 3: Multiply \( ٧ \times ١ = ٧ \). Answer: ٧ not in options, closest is (ج) ١٣ or (أ) ٩, so none exact. Final answers summary: 1) Domain: \( [-٣, \infty) \) 2) Limit: 0 (not listed) 3) Radius: ٣ سم 4) \( (ع + د)(س) = س^٢ - ٤ \) 5) Limit: غير معرفة 6) \( ب = ٠.٥٤ \) 7) \( (د * ر)(٢) = ٧ \)