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JEE Main Limits and Derivatives — practice questions — page 2

Explore 55 free Limits and Derivatives questions in JEE Main Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Limits and Derivatives questions and exercises with answers

Showing questions 31–55 of 55.

If the two one sided limits differ, the limit at that point:Read the answer and worked solution →To find a limit at 5, one looks at values of x that are:Read the answer and worked solution →A limit describes the behaviour of a function:Read the answer and worked solution →The derivative of a function at a point is defined using a:Read the answer and worked solution →The definition of derivative applies to a function that is:Read the answer and worked solution →Defining the derivative directly from the limit is called the:Read the answer and worked solution →The derivative exists at a point only if the limit:Read the answer and worked solution →The derivative at a point gives the slope of the:Read the answer and worked solution →Velocity at a single instant of time is called:Read the answer and worked solution →Instantaneous velocity is found by taking a limit of the:Read the answer and worked solution →For the function x plus 10, the limit at 5 works out to:Read the answer and worked solution →Points such as 4.9, 4.95 and 4.99 lie to the left of:Read the answer and worked solution →A limit is concerned with the value a function is:Read the answer and worked solution →Derivatives are defined at a point lying in the function's:Read the answer and worked solution →The two one sided limits of a function are compared to test:Read the answer and worked solution →Reading the derivative as a rate of change describes how fast a value:Read the answer and worked solution →The first principle finds a derivative without using any:Read the answer and worked solution →True or false on limitsRead the answer and worked solution →Quick picks on limitsRead the answer and worked solution →Match each term to its meaningRead the answer and worked solution →Limit exists or notRead the answer and worked solution →Limit or derivativeRead the answer and worked solution →Test a limit at a pointRead the answer and worked solution →Fill the gaps on limitsRead the answer and worked solution →Spot the one that does not fitRead the answer and worked solution →

Worked practice questions

If the two one sided limits differ, the limit at that point:

  1. Equals the left
  2. Equals the right
  3. Equals to zero
  4. Does not exist
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Correct answer: D. Does not exist

1. The two sides disagree about what value is expected. 2. No single common value can be picked. 3. So the limit does not exist at that point. _Source: syllabus Mathematics, Chapter 13, Limits and Derivatives._

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To find a limit at 5, one looks at values of x that are:

  1. Near five
  2. Near zero
  3. Near nine
  4. Near ten
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Correct answer: A. Near five

1. The limit describes behaviour close to the point. 2. Values such as 4.9, 4.95 and 4.99 are tried. 3. So x is taken near five. _Source: syllabus Mathematics, Chapter 13, Limits and Derivatives._

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A limit describes the behaviour of a function:

  1. At the origin
  2. Near a point
  3. At infinity
  4. Over all x
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Correct answer: B. Near a point

1. The value of the function at the point itself is not the issue. 2. What matters is what happens close by. 3. So a limit describes behaviour near a point. _Source: syllabus Mathematics, Chapter 13, Limits and Derivatives._

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