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AP Intermediate 2nd Year Continuity, Differentiability & Derivatives — practice questions — page 6

Explore 165 free Continuity, Differentiability & Derivatives questions in AP Intermediate 2nd Year 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 151–165 of 165.

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 →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Flip and pair: rule with what it handlesRead the answer and worked solution →The second derivative testRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Tap every point you must test for an absolute maximumRead the answer and worked solution →Which way does the implication run?Read the answer and worked solution →Assertion and reason: continuityRead the answer and worked solution →Local or absolute?Read the answer and worked solution →Continuous or not?Read the answer and worked solution →Order the continuity checkRead the answer and worked solution →Assertion and reason: rates of changeRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →

Worked practice questions

The chain rule can be extended to composites of:

  1. More functions
  2. Only two ever
  3. Only three eve
  4. No functions a
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Correct answer: A. More functions

1. The rule multiplies the rates along the composition. 2. That pattern keeps going for longer chains. 3. Readers are invited to formulate it for more functions. 4. So the answer is more functions. _Source: syllabus Mathematics, Ch 5 'Continuity and Differentiability'_

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Composites of continuous functions, by Theorem 2, are:

  1. Undefined a
  2. Unbounded a
  3. Continuous
  4. Discontinuo
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Correct answer: C. Continuous

1. The theorem applies to f o g defined at c. 2. Both inner and outer functions are continuous. 3. So their composite is continuous too. 4. The answer is continuous. _Source: syllabus Mathematics, Ch 5 'Continuity and Differentiability'_

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For f(x) = 2x + 3 at x = 1, the limit and f(1) are both:

  1. 2
  2. 7
  3. 5
  4. 3
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Correct answer: C. 5

1. Substituting x = 1 gives 2 times 1 plus 3. 2. The limit as x tends to 1 gives the same. 3. Both come out as 5, so f is continuous there. 4. The answer is 5. _Source: syllabus Mathematics, Ch 5 'Continuity and Differentiability'_

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