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Questions and Answers

Find the domain of the function $ rac{1}{3x^{2} - 27}$

  • x > 3
  • x ≠ -3
  • x < -3
  • x ≠ 3 (correct)
  • Find the difference quotient of f(x) = 3x^3 - 5x

  • 3x^2 - 5 (correct)
  • 9x^2 - 5
  • 3x^2 + 5
  • 9x^2 + 5
  • Find C(x) = g(f(x)), given f(x) = 4x^3 and g(x) = 2x - 5

  • 8x^3 + 10x + 5
  • 8x^3 - 10x - 5 (correct)
  • 8x^3 - 10x + 5
  • 8x^3 + 10x - 5
  • How can the graph of $ rac{1}{5}f(x-5)-2$ be obtained from the graph of f(x)?

    <p>Shift 5 units to the right, stretch vertically by a factor of 5, and shift 2 units downward</p> Signup and view all the answers

    What transformations are needed to sketch the graph of the given function?

    <p>Shift 5 units to the right and 2 units downward</p> Signup and view all the answers

    What is the purpose of finding the difference quotient?

    <p>To find the average rate of change of a function</p> Signup and view all the answers

    What is the domain of the function f(x) = 4x^3?

    <p>All real numbers</p> Signup and view all the answers

    Which equation represents Galileo's law for the speed of a falling object?

    <p>f(t) = 4.9t2</p> Signup and view all the answers

    What is the initial height of the ball when it is dropped from the CN Tower observation deck?

    <p>450m</p> Signup and view all the answers

    What is the average rate of speed of the ball from time t=5 to t=5.1 seconds?

    <p>4.9 m/s</p> Signup and view all the answers

    What is the average rate of speed of the ball from time t=5 to t=5.01 seconds?

    <p>4.9 m/s</p> Signup and view all the answers

    What is the average rate of speed of the ball from time t=5 to t=5.001 seconds?

    <p>4.9 m/s</p> Signup and view all the answers

    What does the average rate of speed of the ball seem to be approaching as t approaches 5 seconds?

    <p>4.9 m/s</p> Signup and view all the answers

    What is the average rate of speed of the ball from time t=5 to t=5.1 seconds in km/h?

    <p>176.4 km/h</p> Signup and view all the answers

    What is the average rate of speed of the ball from time t=5 to t=5.01 seconds in km/h?

    <p>176.4 km/h</p> Signup and view all the answers

    Which mathematician is credited with creating stochastic calculus during World War II?

    <p>Kiyosi Itô</p> Signup and view all the answers

    What is the main benefit of the Stratonovich integral in stochastic calculus?

    <p>It obeys the usual chain rule</p> Signup and view all the answers

    Which stochastic process is commonly used for modeling Brownian motion and diffusion processes in space?

    <p>Wiener process</p> Signup and view all the answers

    Which integral is defined for a semimartingale X and a locally bounded predictable process H?

    <p>Itô integral</p> Signup and view all the answers

    What is the alternative notation used to denote the Stratonovich integral?

    <p>∫ 0 t X s ∂ Y s</p> Signup and view all the answers

    In which field is stochastic calculus commonly applied?

    <p>Mathematical finance</p> Signup and view all the answers

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