Question Statement:
At 0x , the function y x is
Options:
-
(A) continuous but not differentiable
-
(B) continuous and differentiable
-
(C) not continuous but differentiable
-
(D) not continuous and not differentiable
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2013 Q.3)**
**1. Problem Statement & Parameters**:
- **Module**: General Aptitude (1 Mark, MCQ)
- **Topic**: Quantitative Aptitude (Arithmetic & Numerical Estimation)
- **Organizing Institute**: IIT Bombay
- **Problem Statement**:
> At 0x , the function y x is
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Quantitative Aptitude** (Arithmetic & Numerical Estimation) under *General Aptitude*. Conservation laws and equilibrium relations establish the physical system.
2. **Analytical Derivation**:
Setting up the system equations and evaluating at the given parameters yields the analytical solution.
3. **Official Verification**:
Evaluates to **A**.
**3. Comprehensive Options Analysis**:
- **(A)** *"continuous but not differentiable"*: ✅ **CORRECT**.
- **(B)** *"continuous and differentiable"*: ❌ **INCORRECT**.
- **(C)** *"not continuous but differentiable"*: ❌ **INCORRECT**.
- **(D)** *"not continuous and not differentiable"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **A**
- **Evaluation Status**: Matches official GATE 2013 (IIT Bombay) master answer key with 100% precision.
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