Limits & Continuity Basics

Key limits and continuity at a point. Ideal for board exams and competitive test prep.

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QUESTION NO 01

Derivative of a constant is?

Answer: 0

d/dx (c) = 0.

Shahzad Mahota @shahzad-mahota

302 Quizzes

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QUESTION NO 02

Derivative of xⁿ is?

Answer: n xⁿ⁻¹

Power rule: d/dx xⁿ = n xⁿ⁻¹.

Shahzad Mahota @shahzad-mahota

302 Quizzes

2930 Questions

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QUESTION NO 03

Derivative of sin x is?

Answer: cos x

d/dx sin x = cos x.

Shahzad Mahota @shahzad-mahota

302 Quizzes

2930 Questions

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QUESTION NO 04

Derivative of cos x is?

Answer: −sin x

d/dx cos x = −sin x.

Shahzad Mahota @shahzad-mahota

302 Quizzes

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QUESTION NO 05

∫ x dx = ?

Answer: (1/2)x² + C

Antiderivative of x is x²/2 + C.

Shahzad Mahota @shahzad-mahota

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QUESTION NO 06

Limit of (x→0) sin x / x is?

Answer: 1

Standard limit: lim sin x / x = 1.

Shahzad Mahota @shahzad-mahota

302 Quizzes

2930 Questions

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QUESTION NO 07

Derivative of eˣ is?

Answer: eˣ

Exponential eˣ is its own derivative.

Shahzad Mahota @shahzad-mahota

302 Quizzes

2930 Questions

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QUESTION NO 08

Derivative of ln x (x>0) is?

Answer: 1/x

d/dx ln x = 1/x.

Shahzad Mahota @shahzad-mahota

302 Quizzes

2930 Questions

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QUESTION NO 09

A function is continuous at a if?

Answer: lim x→a f(x) = f(a)

Limit equals function value at a.

Shahzad Mahota @shahzad-mahota

302 Quizzes

2930 Questions

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QUESTION NO 10

∫ 1/x dx (x>0) = ?

Answer: ln x + C

Natural log is the antiderivative of 1/x.

Shahzad Mahota @shahzad-mahota

302 Quizzes

2930 Questions

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Limits & Continuity Basics

Derivative of a constant is?

Derivative of xⁿ is?

Derivative of sin x is?

Derivative of cos x is?

∫ x dx = ?

Limit of (x→0) sin x / x is?

Derivative of eˣ is?

Derivative of ln x (x>0) is?

A function is continuous at a if?

∫ 1/x dx (x>0) = ?

Published By

Shahzad Mahota

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Limits & Continuity Basics

Derivative of a constant is?

Explanation

Derivative of xⁿ is?

Explanation

Derivative of sin x is?

Explanation

Derivative of cos x is?

Explanation

∫ x dx = ?

Explanation

Limit of (x→0) sin x / x is?

Explanation

Derivative of eˣ is?

Explanation

Derivative of ln x (x>0) is?

Explanation

A function is continuous at a if?

Explanation

∫ 1/x dx (x>0) = ?

Explanation

Published By

Shahzad Mahota

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