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Limits, Continuity & Derivatives

JEE Mathematics • 10 questions • Free on ExamBattle

Practice Questions

1. Q1

   lim(x→0) [sin(3x) / x] is equal to:

   • A. 0
   • B. 1
   • C. 3
   • D. ∞

2. Q2

   lim(x→0) [(eˣ − 1) / x] is equal to:

   • A. 0
   • B. 1
   • C. e
   • D. ∞

3. Q3

   The derivative of f(x) = x³ − 3x² + 2x − 5 at x = 1 is:

   • A. −3
   • B. 0
   • C. 2
   • D. -1

4. Q4

   If f(x) = sin(x²), then f'(x) is:

   • A. cos(x²)
   • B. 2x cos(x²)
   • C. −2x cos(x²)
   • D. 2x sin(x²)

5. Q5

   The function f(x) = |x − 2| is:

   • A. Differentiable everywhere
   • B. Continuous but not differentiable at x = 2
   • C. Neither continuous nor differentiable at x = 2
   • D. Differentiable everywhere except x = 0

6. Q6

   Using Rolle's theorem, if f(a) = f(b), then there exists c ∈ (a, b) such that:

   • A. f'(c) = f(c)
   • B. f'(c) = 0
   • C. f(c) = 0
   • D. f''(c) = 0

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