The video tutorial explores the concept of derivatives using the limit definition. It focuses on evaluating the derivative at x=1 by examining both left-hand and right-hand limits. The tutorial highlights the discontinuity in the denominator and demonstrates the calculation of derivatives from both sides. It concludes by explaining why the function is not differentiable at x=1 due to differing left and right-hand limits, emphasizing the importance of showing these limits rather than just identifying a corner in the graph.

What is the purpose of using the limit definition in calculus?

• To determine the maximum value of a function

• To calculate the volume of a solid

• To identify the derivative of a function

• To find the area under a curve

What issue arises when evaluating the one-sided limit from the left?

• The denominator has a discontinuity

• The numerator becomes undefined

• The limit does not exist

• The function becomes non-linear

How is the derivative determined when x approaches 1 from the left?

• By finding the average rate of change

• By evaluating the limit of the function

• By calculating the slope of the tangent line

• By using the absolute value of the difference

What is the derivative when x approaches 1 from the right?

• Undefined

• 1

• 0

• -1

Why is the function not differentiable at x equals 1?

• The derivative is zero

• The graph has a corner at that point

• The function is continuous at that point

• The left and right-hand limits are equal