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Indian Navy 10+2 B.Tech Cadet Continuity and Differentiability — practice questions

Explore 23 free Continuity and Differentiability questions in Indian Navy 10+2 B.Tech Cadet Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Continuity and Differentiability questions and exercises with answers

Showing questions 1–23 of 23.

The function $f(x) = |x|$ is continuous everywhere but is NOT differentiable at:Read the answer and worked solution →Complete the definition of continuityRead the answer and worked solution →True or false: continuity and differentiabilityRead the answer and worked solution →Which way does the implication run?Read the answer and worked solution →Tap every operation that preserves continuityRead the answer and worked solution →Combining continuous functionsRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Complete the chain rule ideaRead the answer and worked solution →Flip and pair: rule with what it handlesRead the answer and worked solution →Spot the one that does not belongRead 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 →Where continuity can failRead the answer and worked solution →Which property is stronger?Read the answer and worked solution →True or false: combining functionsRead the answer and worked solution →Flip and pair: condition with what followsRead the answer and worked solution →Spot the odd one outRead the answer and worked solution →Assertion and reason: continuityRead the answer and worked solution →Tap every requirement for continuity at a pointRead the answer and worked solution →Two true, one falseRead the answer and worked solution →Complete the one-way implicationRead the answer and worked solution →

Worked practice questions

The function $f(x) = |x|$ is continuous everywhere but is NOT differentiable at:

  1. $x = -1$
  2. $x = 0$
  3. every point
  4. $x = 1$
Show answer and solution

Correct answer: B. $x = 0$

|x| has a corner at 0: left slope −1, right slope +1, so it is not differentiable there (though continuous).

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Complete the definition of continuity

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Missing parts
  1. Answer
    limit
    Choices
    1. limit
    2. derivative
    3. integral
  2. Answer
    value
    Choices
    1. value
    2. slope
    3. sign
  3. Answer
    domain
    Choices
    1. domain
    2. range
    3. graph
Complete the statement
A real valued function is continuous at a point in its domain if the {0} of the function at that point equals the {1} of the function there. It is continuous outright if this holds on the whole of its {2}.
Continuity at a point compares two things: the limit and the value. Source: syllabus Maths, Ch 5 Continuity and Differentiability.

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True or false: continuity and differentiability

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Questions
  1. Statement is true
    Yes
    Statement
    Every differentiable function is continuous.
  2. Statement is true
    No
    Statement
    Every continuous function is differentiable.
  3. Statement is true
    Yes
    Statement
    The converse of the first statement is not true.
  4. Statement is true
    Yes
    Statement
    Differentiability is the stronger condition.
  5. Statement is true
    Yes
    Statement
    A function can be continuous without being differentiable.
The implication runs one way only, and the chapter says so. Source: syllabus Maths, Ch 5 Continuity and Differentiability.

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