Understanding Limits and Derivatives

The video tutorial explains how to evaluate limits that resemble the definition of a derivative. It covers the derivative of ln(x) using the limit as h approaches 0, the derivative of sin(x) using a similar limit, and the derivative of tan(x) using an alternative definition of the derivative. The tutorial provides step-by-step solutions and highlights the importance of recognizing derivative formulas.

What is the derivative of ln(x)?

• x

• 1/x

• ln(x)

• x^2

Which function's derivative is being evaluated in the second example?

• secant

• cosine

• sine

• tangent

What is the derivative of sine(x)?

• secant

• tangent

• cosine

• sine

What is the alternative definition of the derivative used in the third example?

• f'(a) = limit as h approaches 0 of f(x+h) - f(x) / x - a

• f'(x) = limit as x approaches a of f(x) - f(a) / h

• f'(a) = limit as x approaches a of f(x) - f(a) / x - a

• f'(x) = limit as h approaches 0 of f(x+h) - f(x) / h

In the tangent function example, what is the value of 'a'?

• pi

• pi/4

• pi/6

• pi/3

What is the derivative of tangent(x)?

• secant

• secant squared

• cosine

• sine

What is secant squared pi over six equal to?

• 2/3

• 3/4

• 4/3

• 3/2

What is the cosine of pi over six?

• 1/2

• sqrt(3)/2

• sqrt(2)/2

• 3/2

What is the final answer to the tangent function limit problem?

• 2/3

• 4/3

• 1/3

• 3/4

What is the relationship between secant and cosine?

• Secant is the square of cosine

• Secant is the integral of cosine

• Secant is the reciprocal of cosine

• Secant is the derivative of cosine