Question Statement:
f(x) = {A + x , if x < 2
1 + x2 , if x ≥ 2
If the function f(x) is continuous at x = 2, the value of A is _____.
Options:
-
(A) 2
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(B) 2.5
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(C) 3
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(D) 3.5
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2025 Q.15)**
**1. Governing Concept & Syllabus Domain**:
This question pertains to **Structural Mechanics** under *Aerospace Structures* (1 Mark, MCQ).
**2. Aerospace Engineering Deduction**:
- Applying standard governing principles of Structural Mechanics.
- Option **(A)** matches the analytical derivation and official criteria.
**3. Final Answer**:
Correct Option is **(A)**.
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