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

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

<p>All real numbers (C)</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 (C)</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 (A)</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 (C)</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 (B)</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 (A)</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 (B)</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 (C)</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 (B)</p> Signup and view all the answers

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

<p>Kiyosi Itô (D)</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 (A)</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 (B)</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 (A)</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 (B)</p> Signup and view all the answers

In which field is stochastic calculus commonly applied?

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

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