f(x)=eˣ-1. (A) f diff everywhere ✓. (B) g=(eˣ-1)/x, g(0)=1, diff everywhere ✓. (C) f'(1)=e≠1 ✗. (D) f'(0)=1 ✓. Answer: (A),(B),(D) Key Concept: f(x+y)=f(x)+f(y)+f(x)f(y) ⟹ 1+f is exponential

Limits, Continuity & Differentiability

General

Grade 12

Question:

<p>Which are TRUE?</p>

Step-by-Step Solution

Key Concept: General

<div class="solution"><p>f(x)=eˣ-1. (A) f diff everywhere ✓. (B) g=(eˣ-1)/x, g(0)=1, diff everywhere ✓. (C) f'(1)=e≠1 ✗. (D) f'(0)=1 ✓. <strong>Answer: (A),(B),(D)</strong></p><div class="key-concept"><strong>Key Concept:</strong> f(x+y)=f(x)+f(y)+f(x)f(y) ⟹ 1+f is exponential</div></div>

Correct Answer: A,B,D

Question:

Step-by-Step Solution

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