alleryThe derivative of $\tan x$ with respect to $x$ is:
- $\sec x \tan x$
- $\cot x$
- $\sec^2 x$
- $-\csc^2 x$
Show answer and solution
Correct answer: C. $\sec^2 x$
d/dx(tan x) = sec²x.
AP Calculus AB Unit 1B3: Asymptotic Behavior and Infinite Limits — practice questions — page 2
Explore 75 free Unit 1B3: Asymptotic Behavior and Infinite Limits questions in AP Calculus AB Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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Showing questions 31–60 of 75.
The derivative of $\tan x$ with respect to $x$ is:Read the answer and worked solution →The derivative of $\sqrt{x}$ with respect to $x$ is:Read the answer and worked solution →The decimal expansion of 7/8 is:Read the answer and worked solution →A function $f$ is continuous at a point $c$ if:Read the answer and worked solution →The derivative of $x e^x$ with respect to $x$ is:Read the answer and worked solution →A quadratic polynomial can have at most how many zeroes?Read the answer and worked solution →The zeroes of the polynomial $x^2 - 3x - 4$ are:Read the answer and worked solution →For any two positive integers, HCF × LCM equals:Read the answer and worked solution →The product of any three consecutive positive integers is always divisible byRead the answer and worked solution →A rational number is any number that can be written in the form p/q, where p and q are integers and:Read the answer and worked solution →The exact formula for π was first given as an INFINITE SERIES by which Indian mathematician (14th century)?Read the answer and worked solution →For which of the following fractions will the decimal expansion have a REPEATING (non-terminating) block?Read the answer and worked solution →Aryabhata (499 CE) gave the approximation π ≈ 3927/1250. He also called this an 'āsanna' meaning:Read the answer and worked solution →Whole numbers consist of:Read the answer and worked solution →Which of these is irrational?Read the answer and worked solution →How many natural numbers are there?Read the answer and worked solution →The product of two negative integers is:Read the answer and worked solution →Convert 3/4 to a decimal:Read the answer and worked solution →The product 22/7 × 7 equals:Read the answer and worked solution →The set of natural numbers N starts at:Read the answer and worked solution →Which expression is INCORRECT?Read the answer and worked solution →Which of these is the smallest natural number?Read the answer and worked solution →Convert 0.5 to a fraction:Read the answer and worked solution →The set of real numbers ℝ consists of:Read the answer and worked solution →By Brahmagupta's rules: a fortune (positive) multiplied by a debt (negative) gives:Read the answer and worked solution →Which of these is NOT an equivalent fraction of −1/3?Read the answer and worked solution →By Brahmagupta's laws, what is (−5) − (−3)?Read the answer and worked solution →Find a rational number lying strictly between 1/4 and 1/3:Read the answer and worked solution →Which fraction has a TERMINATING decimal expansion?Read the answer and worked solution →Ancient Indian mathematicians named powers of 10. According to the Vedas, the name for 10¹² was:Read the answer and worked solution →
Worked practice questions
The derivative of $\sqrt{x}$ with respect to $x$ is:
- $\dfrac{1}{2\sqrt{x}}$
- $\dfrac{1}{\sqrt{x}}$
- $2\sqrt{x}$
- $\dfrac{1}{2x}$
Show answer and solution
Correct answer: A. $\dfrac{1}{2\sqrt{x}}$
We have d/dx(x^{1/2}) = ½ x^{−1/2}.
So d/dx(x^{1/2}) = 1/(2√x).
The decimal expansion of 7/8 is:
- non-terminating repeating
- terminating
- not defined
- non-terminating non-repeating
Show answer and solution
Correct answer: B. terminating
8 = 2³ (only prime factor 2), so 7/8 terminates.
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Practise Unit 1B3: Asymptotic Behavior and Infinite Limits →More Mathematics topics
Unit 3B: Implicit Differentiation and Inverse FunctionsUnit 3A: Chain Rule and Composite FunctionsUnit 1A3: Function Composition and InversesUnit 1A1: Relations, Functions and GraphsUnit 1A2: Trigonometric Functions & Inverse TrigUnit 2: Differentiation and Fundamental Derivative RulesUnit 6A: Indefinite Integrals & Fundamental TheoremUnit 1B1: Limit Concepts and Graphical Limits