Start learning →

Indian Navy MR Continuity and Differentiability — practice questions

Explore 23 free Continuity and Differentiability questions in Indian Navy MR Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

Practise Continuity and Differentiability with Quill →

Continuity and Differentiability questions and exercises with answers

Showing questions 1–23 of 23.

By the chain rule, $\dfrac{d}{dx} f(g(x))$ equals: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

By the chain rule, $\dfrac{d}{dx} f(g(x))$ equals:

  1. $f'(g'(x))$
  2. $f'(x)\cdot g'(x)$
  3. $f'(g(x))\cdot g'(x)$
  4. $f'(g(x))$
Show answer and solution

Correct answer: C. $f'(g(x))\cdot g'(x)$

Chain rule: differentiate the outer function at g(x) and multiply by g'(x).

Open this question →

Complete the definition of continuity

Read exercise and reference answers
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.

Open this exercise →

True or false: continuity and differentiability

Read exercise and reference answers
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.

Open this exercise →

How to practise

  1. Choose a Continuity and Differentiability question and try to work out your answer.
  2. Open the question to check the correct answer and read its worked solution.
  3. Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.

More Mathematics topics

Binomial TheoremPermutations and CombinationsProbability & StatisticsSequencesSequences and SeriesGeometryLinear ProgrammingLimits and Continuity