Calculus Limits and Functions

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Questions and Answers

What is the limit of x as x approaches 0?

  • 1
  • Undefined
  • 0 (correct)
  • Infinity

What is the value of the limit of sec(x) as x approaches 0?

  • 1 (correct)
  • 0
  • Infinity
  • -1

What is the behavior of the limit of -tan(x) as x approaches π/2 from the left?

  • Converges to 0
  • Converges to Infinity
  • Converges to -Infinity (correct)
  • Converges to 1

Which limit expression approaches a value, rather than Infinity or Undefined?

<p>lim_{x→0} x (A), lim_{x→0} sec(x) (B)</p> Signup and view all the answers

Which expression represents a limit that is undefined?

<p>lim_{x→π/2⁻} (-tan(x)) (C)</p> Signup and view all the answers

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Study Notes

Limit Expressions

  • The limit of x as x approaches 0 is 0.
  • The limit of sec(x) as x approaches 0 is 1.
  • The limit of -tan(x) as x approaches π/2 from the left is negative infinity
  • The expression x→π/2⁻ indicates that x approaches π/2 from the left side, meaning x values slightly less than π/2.
  • Sec(x) is the reciprocal of cos(x)
  • Tan(x) is the ratio of sin(x) to cos(x)

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