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BIHAR CET Limits and Continuity — practice questions — page 3

Explore 131 free Limits and Continuity questions in BIHAR CET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Limits and Continuity questions and exercises with answers

Showing questions 61–90 of 131.

Complete the definition of a critical pointRead the answer and worked solution →Order the first derivative testRead the answer and worked solution →Match each sign change to its verdictRead the answer and worked solution →The second derivative testRead the answer and worked solution →True or false: maxima and minimaRead the answer and worked solution →Order the working rule for absolute maxima and minimaRead the answer and worked solution →Tap every point you must test for an absolute maximumRead the answer and worked solution →Local or absolute?Read the answer and worked solution →Complete the rate of change statementRead the answer and worked solution →The chain rule for related ratesRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →True or false: increasing and decreasingRead the answer and worked solution →Flip and pair: symbol with meaningRead the answer and worked solution →Match each situation to the right toolRead the answer and worked solution →Tap every statement true of a local maximum at cRead the answer and worked solution →Reading the tests backRead the answer and worked solution →Which test is being described?Read the answer and worked solution →Assertion and reason: rates of changeRead the answer and worked solution →Spot the odd oneRead the answer and worked solution →Complete the second derivative testRead the answer and worked solution →True or false: scope of this chapterRead the answer and worked solution →Match each kind of matrix to its conditionRead the answer and worked solution →Sort each matrix by its shapeRead the answer and worked solution →Tap every matrix that must be squareRead the answer and worked solution →Complete the definition of a matrixRead the answer and worked solution →When is a product defined?Read the answer and worked solution →True or false: transposesRead the answer and worked solution →

Worked practice questions

Complete the definition of a critical point

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Missing parts
  1. Answer
    0
    Choices
    1. 0
    2. 1
    3. undefined
  2. Answer
    not differentiable
    Choices
    1. not differentiable
    2. not continuous
    3. not defined
Complete the statement
A point c in the domain of f is a critical point if either f ′(c) = {0}, or f is {1} at c.
Your syllabus's definition covers two cases, and the second one is the one people forget. Source: syllabus Maths Part I, Ch 6 Application of Derivatives.

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Order the first derivative test

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Steps
  1. Find the critical points where f ′(x) = 0 or f is not differentiable
  2. Check f is continuous at the critical point c
  3. Look at the sign of f ′(x) just to the left of c
  4. Look at the sign of f ′(x) just to the right of c
  5. Read the verdict from whether that sign changed, and how
The test is a sign check either side of the critical point, which is why the order matters. Source: syllabus Maths Part I, Ch 6 Application of Derivatives.

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Match each sign change to its verdict

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Matching pairs
  1. Left
    f ′ goes positive → negative
    Right
    local maximum at c
  2. Left
    f ′ goes negative → positive
    Right
    local minimum at c
  3. Left
    f ′ does not change sign
    Right
    point of inflexion
  4. Left
    f ′(c) = 0 or f not differentiable at c
    Right
    c is a critical point
The three outcomes of the first derivative test, exactly as your syllabus lists them. Source: syllabus Maths Part I, Ch 6 Application of Derivatives.

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