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Continuity and Differentiability — Practice Quiz

ICSE · Class 12 · Mathematics

Try a 4-question quiz on Continuity and Differentiability for ICSE Class 12 Mathematics: tap an answer to check it and see why.

105 questions29 flashcards9 formulas & key relations5 concepts

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A graph of a continuous function at a specific point, showing the limit approaching the function value, illustrating that the function is unbroken and defined at that point.
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Quick Quiz: Continuity and Differentiability

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1

If f(x) = (x² - 9)/(x - 3) for x ≠ 3, and f(3) = k, then the value of k that makes f continuous at x = 3 is:

2

The function f(x) = |x - 2| is:

3

For the function f(x) = {kx² if x ≤ 2, 3 if x > 2} to be continuous at x = 2, the value of k is:

4

Which of the following functions is NOT continuous at x = 0?

105 Questions·
MCQmultiple choice

Sample Questions

1MCQ

The value of lim_{x→0}(sin x / x) is:

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B

lim_{x→0}(sin x / x) = 1 is a standard limit. This is Theorem 8.1(i).

2MCQ

The value of lim_{x→0}(eˣ − 1) / x is:

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C

lim_{x→0}(eˣ−1)/x = 1 is a standard exponential limit (Theorem 8.1(iii)).

3MCQ

lim_{x→0}(tan x / x) equals:

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A

lim_{x→0}(tan x/x) = 1. Since tan x = sin x/cos x and cos x→1 as x→0.

4MCQ

A function f is continuous at x = c if:

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B

The complete definition: f is continuous at c if lim_{x→c}f(x) = f(c), which requires f(c) defined, limit exists, and limit = f(c).

+101 more questions on Continuity and Differentiability (ICSE Class 12 Mathematics)

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Frequently Asked Questions

What are the important topics in Continuity and Differentiability for ICSE Class 12 Mathematics?
Key topics in Continuity and Differentiability include Limits and One-Sided Limits, Continuity at a Point and on an Interval, Algebra of Continuous Functions, Differentiability at a Point and One-Sided Derivatives. Study these first, then practise questions on each for the ICSE Class 12 board exam.
How many practice questions are there for Continuity and Differentiability?
There are 105 questions on Continuity and Differentiability. Try the 4-question sample quiz on this page first; each answer shows an explanation when you tap it.

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Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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