Understanding Limits and L'Hôpital's Rule

The video tutorial explains how to find limits of functions as variables approach certain values, particularly when the limit results in an indeterminate form like 0/0. It introduces L'Hôpital's Rule, which allows the calculation of such limits by differentiating the numerator and denominator. The tutorial provides examples using trigonometric functions and verifies the results graphically. The video aims to help students understand the application of L'Hôpital's Rule in calculus and its graphical interpretation.

What is the indeterminate form of the limit of sin(8x)/tan(3x) as x approaches z?

• 0/1

• 1/0

• ∞/∞

• 0/0

Which rule can be applied to solve limits with indeterminate forms like 0/0?

• Product Rule

• Chain Rule

• L'Hôpital's Rule

• Quotient Rule

What is the derivative of sin(8x)?

• cos(8x)

• 8 cos(8x)

• sin(8x)

• 8 sin(8x)

What is the limit of sin(8x)/tan(3x) as x approaches zero after applying L'Hôpital's Rule?

• 0

• 8/3

• 1

• 3/8

In the new example, what trigonometric identity is used to rewrite secant?

• 1/cotangent

• 1/tangent

• 1/sine

• 1/cosine

What is the indeterminate form of the limit of -2cos(7x)/cos(5x) as x approaches π/2?

• 0/0

• ∞/∞

• 1/0

• 0/1

What is the derivative of -2cos(7x)?

• -14 sin(7x)

• 14 sin(7x)

• 7 sin(7x)

• -7 sin(7x)

What is the value of sin(5π/2) on the unit circle?

• 1

• 0

• √2/2

• -1

What is the value of sin(7π/2) on the unit circle?

• 0

• 1

• -1

• √2/2

What is the final limit of -2cos(7x)/cos(5x) as x approaches π/2 after applying L'Hôpital's Rule?

• -5/14

• 5/14

• -14/5

• 14/5