Find the value a that makes the function continuous

The video tutorial explains the concept of continuity in functions, focusing on evaluating limits from both the left and right sides. It demonstrates how to solve equations to ensure a function is continuous, using a step-by-step approach. The tutorial concludes by verifying the solution and confirming the function's continuity.

What is required for a function to be continuous at a point?

• The function must be defined for all real numbers.

• The function must be differentiable at that point.

• The left-hand and right-hand limits must be equal at that point.

• The function must have a maximum at that point.

When evaluating limits, what is the first step in the process?

• Finding the derivative of the function.

• Substituting values into the function.

• Checking for asymptotes.

• Graphing the function.

What equation is formed when equating the left and right limits in this example?

• 3 - 2A = 2/2 + 1

• 3A + 2 = 1/2

• 2A - 3 = 1

• A/2 + 3 = 2

What is the value of 'a' that makes the function continuous?

• 1/2

• 1

• 2

• 3/2

What is the final step in solving for 'a' in the equation?

• Subtracting 1 from both sides.

• Dividing both sides by -2.

• Multiplying both sides by 2.

• Adding 3 to both sides.