Exploring Limits in Depth: Part 2 Review

The video tutorial covers the average rate of change, explaining it as the difference in y-values over the difference in x-values. It also discusses how to approximate derivatives using tables and limit notations. The power rule is introduced for finding derivatives, with examples provided. The video concludes with a reminder about practice work due on Monday.

What formula is used to calculate the average rate of change?

• Y1 - Y2 / X1 - X2

• X2 - X1 / Y2 - Y1

• Y2 - Y1 / X2 - X1

• X1 + X2 / Y1 + Y2

How do you approximate a derivative using a table?

• By finding the slope between two points

• By adding the Y values of two points

• By multiplying the X and Y values of a single point

• By subtracting the X values of two points

What is the limit definition of a derivative?

• Limit as X approaches 0 of (f(x+h) - f(x-h)) / 2h

• Limit as H approaches 0 of f(x) / h

• Limit as X approaches infinity of f(x)

• Limit as H approaches 0 of (f(x+h) - f(x)) / h

How is the derivative of a function evaluated at a specific point?

• By plotting the function and measuring the slope at the point

• By integrating the function and evaluating at the given point

• By applying the power rule and substituting the point into the derivative

• By finding the area under the curve at that point

What is the significance of the number in front of H when finding a derivative?

• It indicates the point at which the derivative is evaluated

• It represents the slope of the tangent line

• It is used to calculate the area under the curve

• It determines the amplitude of the function

In the context of derivatives, what does 'f prime of a number' refer to?

• The maximum value of the function

• The slope of the curve at that number

• The integral of the function at that number

• The area under the curve up to that number

What does the derivative of a function tell us about the function at a specific point?

• The total distance traveled by the function

• The instantaneous rate of change at that point

• The average rate of change between two points

• The cumulative sum of the function's values

What does the limit as X approaches C of (f(x) - f(c)) / (x - c) represent?

• The total change in function from x to c

• The instantaneous rate of change at x = c

• The average rate of change as x approaches c

• The slope of the tangent line at x = c

How can L'Hôpital's rule be applied to find a limit?

• By differentiating the numerator and denominator separately and taking the limit

• By adding the numerator to the denominator and finding the limit

• By integrating the numerator and denominator separately

• By multiplying the numerator and denominator by the highest power of x

What is the result of the derivative of cosine of x evaluated at pi/2?

• 1

• 0

• -1

• Undefined