Approximating Limits Graphically

What value does the limit of (1+x)^(1/x) approach as x gets closer to 0?

• Approximately 3.14

• Exactly 2

• Approximately 2.718

• Exactly 1

What graphical feature did the calculator show for the function (1+x)^(1/x) as x approaches 0?

• An exponential curve

• A straight line

• A parabola

• A hole in the graph

What does the presence of a hole in a graph indicate about the function?

• The function has a minimum value at that point.

• The function intersects with another function.

• The function has a maximum value at that point.

• The function is undefined at that point.

What is the significance of using scientific notation to represent x values when zooming in on a graph?

• It indicates very large numbers.

• It shows the precision of the calculator.

• It simplifies the graphing process.

• It represents very small numbers close to zero.

What is the estimated limit of the function (1+x)^(1/x) as x approaches 0?

• 0

• 1

• pi (approximately 3.14159)

• e (approximately 2.718)

Why can't we directly substitute 0 into the expression (1+x)^(1/x)?

• It simplifies the expression too much.

• It cancels out the x variable.

• It makes the limit equal to 1.

• It results in an undefined expression.

Why is it necessary to use a graphical approach to approximate some limits?

• To visually confirm the limit's value.

• Because algebraic techniques are always insufficient.

• When direct substitution or algebraic techniques don't apply.

• Graphical methods are easier to understand.

Why can't we directly substitute 0 into the expression sin(x)/x?

• It makes the limit equal to 0.

• It results in a division by zero.

• It cancels out the sin(x) term.

• It simplifies the expression too much.

What mode must the calculator be in to graph the function sin(x)/x?

• Scientific mode

• Graphing mode

• Radian mode

• Degree mode

As x approaches 0, what does the y-value of sin(x)/x get closer to?

• 0

• 0.5

• 1

• 1.5