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AP Intermediate 2nd Year Continuity, Differentiability & Derivatives — practice questions — page 3

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 61–90 of 165.

The rule for differentiating a composite function is the:Read the answer and worked solution →f(x) = x squared at x = 0 is:Read the answer and worked solution →Functions written with y not isolated are called:Read the answer and worked solution →Continuity of f at c requires the limit at c to equal:Read the answer and worked solution →Theorem 1 concerns two functions that are both:Read the answer and worked solution →Theorem 2 deals with which kind of function?Read the answer and worked solution →Theorem 3 says differentiability at a point implies:Read the answer and worked solution →Does continuity at a point guarantee differentiability?Read the answer and worked solution →The chain rule can be extended to composites of:Read the answer and worked solution →An alternative to repeated product rule for many factors is: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 →The function f(x) = |x| at x = 0 is continuous but not:Read the answer and worked solution →To differentiate an implicit relation you use the:Read the answer and worked solution →A function that fails the limit test at a point is:Read the answer and worked solution →Composites of continuous functions, by Theorem 2, are:Read the answer and worked solution →Match the calculus ideaRead the answer and worked solution →True or false about continuityRead the answer and worked solution →Continuous or not?Read the answer and worked solution →Order the continuity checkRead the answer and worked solution →Complete the theoremRead the answer and worked solution →Which rule or theorem?Read the answer and worked solution →Continuity valuesRead the answer and worked solution →Continuity bingoRead the answer and worked solution →An alternative to repeated product rule for many factors is:Read the answer and worked solution →True or false about continuityRead the answer and worked solution →Match the calculus ideaRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →The rule for differentiating a composite function is the:Read the answer and worked solution →Order the test for continuity at a pointRead the answer and worked solution →True or false: reading the definitionsRead the answer and worked solution →

Worked practice questions

The rule for differentiating a composite function is the:

  1. Chain rule
  2. Power rule
  3. Prime rule
  4. Cross rule
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Correct answer: A. Chain rule

1. A composite function is a function of a function. 2. Its derivative multiplies the two rates. 3. That is the chain rule. 4. So the answer is the chain rule. _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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Functions written with y not isolated are called:

  1. Inverted
  2. Reflected
  3. Implicit
  4. Explicit
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Correct answer: C. Implicit

1. Sometimes y cannot be written alone on one side. 2. The relation still defines y in terms of x. 3. Such functions are implicit functions. 4. So the answer is implicit. _Source: syllabus Mathematics, Ch 5 'Continuity and Differentiability'_

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