Understanding Limits at Infinity

The video tutorial explains how to determine the limits of an exponential function as x approaches both negative and positive infinity. It analyzes the behavior of the function by examining the exponent and provides example calculations for specific x values. The tutorial concludes with a graphical verification of the limits, showing that the function values increase without bound and approach positive infinity in both cases.

What is the function f(x) discussed in the video?

• f(x) = e^(x^2 - 5)

• f(x) = e^(2x^2 - 5)

• f(x) = e^(x^2 + 5)

• f(x) = e^(2x - 5)

As x approaches negative infinity, what happens to the exponent of e?

• It increases without bound.

• It remains constant.

• It decreases without bound.

• It oscillates.

What is the function value at x = -100?

• e^20000

• e^19995

• e^10000

• e^19990

As x approaches positive infinity, what happens to the function values?

• They decrease without bound.

• They remain constant.

• They oscillate.

• They increase without bound.

What is the behavior of the exponent on e as x approaches positive infinity?

• It oscillates.

• It remains constant.

• It increases without bound.

• It decreases without bound.

What is the function value at x = 100?

• e^10000

• e^20000

• e^19990

• e^19995

What does the graph of the function show as x approaches negative infinity?

• The function values decrease without bound.

• The function values oscillate.

• The function values remain constant.

• The function values increase without bound.

What does the graph of the function show as x approaches positive infinity?

• The function values decrease without bound.

• The function values oscillate.

• The function values remain constant.

• The function values increase without bound.

What is the significance of squaring x in the function?

• It makes the exponent negative.

• It ensures the exponent is always positive.

• It makes the exponent zero.

• It has no effect on the exponent.

What is the overall conclusion about the limits at infinity for the function?

• Both limits oscillate.

• Both limits approach positive infinity.

• Both limits remain constant.

• Both limits approach negative infinity.