Definite Integrals Properties Quiz

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Questions and Answers

At the point (2, 8), if the chain rule was not used during differentiation, what would be the result?

  • 1 - 3y^2
  • 1 + y^3
  • 1 - x^2
  • 1 + 2/3y (correct)

What would be the result of differentiating x^5 − 5x if the chain rule was not used?

  • 5x^4 - 5
  • x^4 - 5
  • x^4 - x^5
  • 5x^4 - ln(5)x (correct)

If the power rule was wrongly applied to the exponential function 5x, what would be the incorrect response?

  • x * 5^(x-1)dx (correct)
  • 5x^(4) - (ln 5)5x
  • (ln a)ax
  • 5x^(5-1)

In the context provided, what might lead to the response x^4 - x^5?

<p>Misapplication of the power rule (D)</p> Signup and view all the answers

If x = 2 and y = 8 satisfy an equation, what could result from calculating 3 dy/dx?

<p>(1 + y)/(3dy) (B)</p> Signup and view all the answers

What would be the outcome of taking the antiderivative of x^5 − 5x?

<p>(1/6)x^6 - (5/2)x^2 + C (C)</p> Signup and view all the answers

What happens if the derivative of a^x is incorrectly taken as a^x instead of (ln a)a^x?

<p>(a - ln a)a^x (B)</p> Signup and view all the answers

If the problem is treated like the limit of a rational function as x goes to infinity, what might lead to an incorrect response?

<p>(e + f)/x (D)</p> Signup and view all the answers

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