Calculus Preliminaries and Function Graphs

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Questions and Answers

What is the geometric representation of real numbers?

  • Circle
  • Parabola
  • Coordinate plane
  • Number line (correct)

Which set of numbers includes non-ending, non-repeating decimals?

  • Rational Numbers (Q)
  • Irrational Numbers (Qc) (correct)
  • Whole Numbers
  • Integers (Z)

What is the symbol used to denote the real number system or the real line?

  • Q
  • Z
  • W
  • R (correct)

What do we call the quotient of any two integers?

<p>Rational Numbers (Q) (A)</p> Signup and view all the answers

Which mathematical concept is viewed in the preliminary chapter before beginning calculus?

<p>Real number system (C)</p> Signup and view all the answers

What is the geometric representation of real numbers?

<p>Points on the number line (A)</p> Signup and view all the answers

Which set of numbers includes non-ending, non-repeating decimals?

<p>Irrational Numbers (B)</p> Signup and view all the answers

What is the symbol used to denote the real number system or the real line?

<p>ℜ (B)</p> Signup and view all the answers

Which mathematical concept is viewed in the preliminary chapter before beginning calculus?

<p>Real number system (B)</p> Signup and view all the answers

What do we call the quotient of any two integers?

<p>Rational Numbers (D)</p> Signup and view all the answers

In which set do the numbers {., −2, −1, 0, 1, 2,.} belong?

<p>Integers (Z) (C)</p> Signup and view all the answers

What are numbers that can be expressed as decimals called?

<p>Rational Numbers (Q) (C)</p> Signup and view all the answers

What is the quotient of any two integers called?

<p>Rational Numbers (Q) (A)</p> Signup and view all the answers

"What is the Real line shown in figure 1.1 used to represent?"

<p>The real number system (C)</p> Signup and view all the answers

What is the limit of the function $f(x) = \frac{x^2 - 1}{x - 1}$ as $x$ approaches 1?

<p>$2$ (D)</p> Signup and view all the answers

Which of the following is the correct derivative of the function $g(x) = \frac{1}{x}$?

<p>$-\frac{1}{x^2}$ (B)</p> Signup and view all the answers

What is the derivative of the function $h(x) = e^{3x}$?

<p>$3e^{3x}$ (A)</p> Signup and view all the answers

What is the value of $\lim_{x \to 0} \frac{\sin(x)}{x}$?

<p>$1$ (D)</p> Signup and view all the answers

Which of the following represents the correct derivative of the function $k(x) = \ln(x^2)$?

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What is the limit of the function $p(x) = \frac{2x^3 - 5x^2 + 3x - 1}{x^2 - 3x + 2}$ as $x$ approaches 2?

<p>$5$ (D)</p> Signup and view all the answers

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