Calculus Concepts and Function Analysis
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Questions and Answers

What is the range of the function $f(x) = |x|$?

  • [0, ∞) (correct)
  • (-∞, 0)
  • (0, ∞)
  • (-∞, ∞)
  • What does it mean for a function to be continuous at $x = c$?

  • limx→c f(x) exists and is finite (correct)
  • limx→c f(x) = ∞
  • All of these
  • f(c) is greater than zero
  • If $f(x) = |x|$, which statement about $f(x)$ is true?

  • f(x) can be classified under neither category
  • f(x) is neither odd nor even
  • f(x) is an odd function
  • f(x) is an even function (correct)
  • What is the value of $ ext{lim}_{x o 0} rac{1 - ext{cos} x}{x^2}$?

    <p>1/2</p> Signup and view all the answers

    A Taylor series expansion is valid only if it is:

    <p>Convergent</p> Signup and view all the answers

    If $c ext{ is in } D$ and $f'(c) = 0$, then the point $c$ is called:

    <p>Critical value</p> Signup and view all the answers

    What is the result of the integral $ ext{int} rac{a e^{mx}}{m} ext{ dx}$?

    <p>$ rac{a e^{mx}}{m} + c$</p> Signup and view all the answers

    The inequality $ax + by ext{ ≤ } c$ when $a = 0$ represents which half-plane?

    <p>Lower half plane</p> Signup and view all the answers

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