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CUET UG Continuity, Differentiability & Derivatives — practice questions — page 2

Explore 36 free Continuity, Differentiability & Derivatives questions in CUET UG Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Continuity, Differentiability & Derivatives questions and exercises with answers

Showing questions 31–36 of 36.

If f is not continuous at c, then c is called a point of:Read the answer and worked solution →f(x) = x squared at x = 0 is:Read the answer and worked solution →The function f(x) = |x| at x = 0 is continuous but not:Read the answer and worked solution →The chain rule can be extended to composites of:Read the answer and worked solution →Composites of continuous functions, by Theorem 2, are:Read the answer and worked solution →For f(x) = 2x + 3 at x = 1, the limit and f(1) are both:Read the answer and worked solution →

Worked practice questions

If f is not continuous at c, then c is called a point of:

  1. Convergence a
  2. Discontinuity
  3. Differentiabil
  4. Integrability a
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Correct answer: B. Discontinuity

1. Continuity can fail at a particular point. 2. That point gets its own name. 3. It is called a point of discontinuity. 4. So the answer is discontinuity. _Source: syllabus Mathematics, Ch 5 'Continuity and Differentiability'_

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f(x) = x squared at x = 0 is:

  1. Not a functi
  2. Continuous
  3. Discontinuo
  4. Undefined a
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Correct answer: B. Continuous

1. Work out the limit of x squared as x tends to 0. 2. That limit is 0, which equals f(0). 3. So the function is continuous at x = 0. 4. The answer is continuous. _Source: syllabus Mathematics, Ch 5 'Continuity and Differentiability'_

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The function f(x) = |x| at x = 0 is continuous but not:

  1. Defined there
  2. Real valued at
  3. Bounded there
  4. Differentiable
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Correct answer: D. Differentiable

1. The graph of the modulus function has a sharp corner. 2. You can draw it without lifting the pen. 3. But no single tangent exists at the corner. 4. So it is continuous but not differentiable. _Source: syllabus Mathematics, Ch 5 'Continuity and Differentiability'_

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