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Limits Continuity Differentiation Questions for AGNIVEER VAYU

Free, AI-curated practice for the Limits Continuity Differentiation section of AGNIVEER VAYU. We have 16+ verified questions in this bank. Below: 5 sample questions. Sign up free to unlock unlimited practice + AI explanations + per-topic analytics.

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Sample questions

Q1 · medium · AI-verified
If f(x) = sin²x + cos²x, then f'(x) is:
  1. −1
  2. 1
  3. 2 sin x cos x
  4. 0
Q2 · medium · AI-verified
What is the value of lim(x→0) (sin 3x) / (5x)?
  1. 0
  2. 1
  3. 3/5
  4. 5/3
Q3 · medium · AI-verified
If y = x^(sin x), then which method is used to find dy/dx?
  1. Quotient rule
  2. Logarithmic differentiation
  3. Chain rule directly
  4. Product rule
Q4 · medium · AI-verified
If f(x) = x³ − 4x² + 5x − 2, what is f'(2)?
  1. −1
  2. 3
  3. 0
  4. 1
Q5 · medium · AI-verified
What is the derivative of tan⁻¹(x) with respect to x?
  1. 1 / (1 + x²)
  2. 1 / √(1 − x²)
  3. 1 / (1 − x²)
  4. −1 / (1 + x²)
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