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NDA Limits and Derivatives — practice questions

Explore 17 free Limits and Derivatives questions in NDA Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Limits and Derivatives questions and exercises with answers

Showing questions 1–17 of 17.

lim(x→0) (sin x) / x equals:Read the answer and worked solution →If f(x) = x², then f′(x) is:Read the answer and worked solution →d/dx (sin x) is:Read the answer and worked solution →d/dx (cos x) is:Read the answer and worked solution →If f(x) = c (a constant), then f′(x) is:Read the answer and worked solution →lim(x→1) (x² − 1) / (x − 1) equals:Read the answer and worked solution →lim(x→0) (1 − cos x) / x² equals:Read the answer and worked solution →If f(x) = 3x² + 5x + 7, then f′(x) is:Read the answer and worked solution →d/dx [(x² + 1)(x + 1)] using product rule equals:Read the answer and worked solution →lim(x→0) (tan x) / x equals:Read the answer and worked solution →lim(x→0) (e^x − 1) / x equals:Read the answer and worked solution →The derivative of f(x) = √x with respect to x is:Read the answer and worked solution →lim(x→2) (x³ − 8) / (x² − 4) equals:Read the answer and worked solution →If f(x) = 1/x, then f′(x) is:Read the answer and worked solution →lim(x→∞) (3x² + x + 1) / (5x² + 2) equals:Read the answer and worked solution →Key in the limitRead the answer and worked solution →Which one does NOT belong?Read the answer and worked solution →

Worked practice questions

lim(x→0) (sin x) / x equals:

  1. 0
  2. 1
  3. x
  4. ∞
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Correct answer: B. 1

1. This is the fundamental trigonometric limit: lim(x→0) (sin x)/x = 1. 2. Used as a starting point to derive d/dx (sin x) = cos x. 3. Holds with x in RADIANS. _Source: syllabus Maths Ch 13 "Limits and Derivatives", §13.2 Limits_

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If f(x) = x², then f′(x) is:

  1. x
  2. 2x
  3. x²
  4. 2x²
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Correct answer: B. 2x

1. Power rule: d/dx (xⁿ) = n xⁿ⁻¹. 2. For n = 2: d/dx (x²) = 2 x. _Source: syllabus Maths Ch 13 §13.4 Derivative — Power Rule_

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d/dx (sin x) is:

  1. cos x
  2. − cos x
  3. tan x
  4. − sin x
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Correct answer: A. cos x

1. d/dx (sin x) = cos x. 2. Companions: d/dx (cos x) = −sin x; d/dx (tan x) = sec²x. _Source: syllabus Maths Ch 13 §13.4 Trig Derivatives_

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