GATE BT 2014 • Q14
NAT • 2 Marks
Section 2: General Biotechnology
Biomolecules, enzyme kinetics
Subtopic: Fundamentals of Biomolecules, enzyme kinetics
Question Statement:
A bacterium belonging to cocci group has a diameter of 2 µm. The numerical value of the ratio of
its surface area to volume (in µm-1) is ________
Step-by-Step Solution & Explanation
### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2014 Q.14)**
**1. Governing Concept & Definition**:
- **Topic**: Engineering Mathematics & Limits of Oscillating Decaying Functions
- Evaluating:
$\lim_{t \to \infty} e^{-2t} \sin(t)$
**2. Detailed Step-by-Step Calculation**:
- By the Squeeze Theorem:
$-1 \le \sin(t) \le 1 \implies -e^{-2t} \le e^{-2t} \sin(t) \le e^{-2t}$
- As $t \to \infty$, $e^{-2t} \to 0$:
$\lim_{t \to \infty} (-e^{-2t}) = 0 \quad \text{and} \quad \lim_{t \to \infty} e^{-2t} = 0$
- Therefore:
$\lim_{t \to \infty} e^{-2t} \sin(t) = 0$
**3. Final Answer**:
- **Calculated Value**: **0**
- **Official GATE Accepted Range**: **0 to 0**
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.
Launch CBT Mock Test