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AP Calculus AB Unit 1B3: Asymptotic Behavior and Infinite Limits — practice questions

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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Unit 1B3: Asymptotic Behavior and Infinite Limits questions and exercises with answers

Showing questions 1–30 of 75.

The unit digit of $7^{2026}$ isRead the answer and worked solution →Which of the following is NOT a polynomial?Read the answer and worked solution →The number of trailing zeros at the end of $50!$ isRead the answer and worked solution →The prime factorisation of 156 is:Read the answer and worked solution →The decimal expansion of 1/3 is:Read the answer and worked solution →The degree of a polynomial is:Read the answer and worked solution →A polynomial of degree 3 is called a:Read the answer and worked solution →Two positive integers have HCF 9 and LCM 90. If one number is 18, the other isRead the answer and worked solution →The number √2 is:Read the answer and worked solution →If $p$ is a prime and $p \mid a^2$, then which must be true?Read the answer and worked solution →A rational number p/q (in lowest terms) has a terminating decimal expansion if the prime factors of q are:Read the answer and worked solution →For a quadratic $ax^2 + bx + c$, the product of its zeroes is:Read the answer and worked solution →The Fundamental Theorem of Arithmetic states that every composite number can be expressed as:Read the answer and worked solution →A cubic polynomial can have at most how many zeroes?Read the answer and worked solution →The sum √3 + √5 is:Read the answer and worked solution →The HCF of 6 and 20 is:Read the answer and worked solution →A polynomial of degree 1 is called a:Read the answer and worked solution →The derivative of $e^x$ with respect to $x$ is:Read the answer and worked solution →If $f(x)=x^2+3x$, then $f'(x)$ equals:Read the answer and worked solution →For $p(x) = x^2 - 3x - 4$, the value of $p(2)$ is:Read the answer and worked solution →If $\text{HCF}(a, b) = 12$ and $\text{LCM}(a, b) = 180$, then the number of possible ordered pairs $(a, b)$ isRead the answer and worked solution →Euclid's division lemma states that for positive integers a and b, there exist unique q and r such that:Read the answer and worked solution →The zeroes of a polynomial $p(x)$ are the values of $x$ for which:Read the answer and worked solution →The derivative of $\log_e x$ with respect to $x$ is:Read the answer and worked solution →By the chain rule, $\dfrac{d}{dx} f(g(x))$ equals:Read the answer and worked solution →The function $f(x) = |x|$ is continuous everywhere but is NOT differentiable at:Read the answer and worked solution →The derivative of $e^{2x}$ with respect to $x$ is:Read the answer and worked solution →The derivative of $\log_e(x^2)$ with respect to $x$ is:Read the answer and worked solution →A function $f$ is continuous at $c$ only if the left-hand limit, right-hand limit and $f(c)$ are:Read the answer and worked solution →Rolle's theorem requires that $f$ be continuous on $[a,b]$, differentiable on $(a,b)$ and:Read the answer and worked solution →

Worked practice questions

The unit digit of $7^{2026}$ is

  1. 1
  2. 7
  3. 3
  4. 9
Show answer and solution

Correct answer: D. 9

Unit digits of powers of 7 cycle with period 4: $7,9,3,1$. Since $2026 \equiv 2 \pmod 4$, the unit digit matches $7^2 = 49$, i.e. 9.

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Which of the following is NOT a polynomial?

  1. $2x - 3$
  2. $x^2 + 5$
  3. $x^3 - 1$
  4. $\dfrac{1}{x-1}$
Show answer and solution

Correct answer: D. $\dfrac{1}{x-1}$

1/(x−1) has the variable in the denominator, so it is not a polynomial.

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The number of trailing zeros at the end of $50!$ is

  1. 12
  2. 13
  3. 11
  4. 10
Show answer and solution

Correct answer: A. 12

Trailing zeros are governed by the power of 5 in $50!$: $\lfloor 50/5 \rfloor + \lfloor 50/25 \rfloor = 10 + 2 = 12$. (Powers of 2 are more plentiful, so 5 is the limiting factor.)

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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