Understanding Limits and Derivatives

The video tutorial explains the cosine function and its graph, focusing on the limit as h approaches 0 for the expression g(pi + h) - g(pi) over h. It describes the slope of the secant line and how it approaches the tangent line at x = pi. The tutorial also discusses alternative methods for calculating limits, including using a calculator to evaluate small values of h.

What is the function g(x) defined as in the video?

• g(x) = sin(x)

• g(x) = tan(x)

• g(x) = cos(x)

• g(x) = x^2

What is the expression for the limit as h approaches 0?

• (g(pi + h) + g(pi)) / h

• (g(pi + h) - g(pi)) / h

• (g(pi) - g(pi + h)) / h

• (g(pi) * g(pi + h)) / h

What does the slope of the secant line represent as h approaches 0?

• The slope of a tangent line

• The slope of a vertical line

• The slope of a diagonal line

• The slope of a horizontal line

What is the slope of the tangent line at x = pi?

• 0

• -1

• Undefined

• 1

What is the value of cosine at x = pi?

• Undefined

• -1

• 1

• 0

What is the nature of the tangent line at x = pi?

• Diagonal

• Horizontal

• Curved

• Vertical

Which method is suggested for evaluating the limit without algebraic tools?

• Using a graph

• Using a ruler

• Using a protractor

• Using a calculator

What happens to the value of the expression as h becomes very small?

• It approaches 0

• It approaches 1

• It approaches -1

• It becomes undefined

What mode should the calculator be in to evaluate trigonometric functions correctly?

• Decimal mode

• Fraction mode

• Radian mode

• Degree mode

What is the result of evaluating the limit with a very small h, such as 0.0001?

• 5 times 10 to the negative 5th

• 1

• 5 times 10 to the positive 5th

• 0.5