Understanding Limits at Infinity

The video tutorial covers the concept of limits at infinity, focusing on functions like 1/x, 1/x^2, and rational functions. It explains how to determine limits as x approaches infinity or negative infinity, using examples and graphing techniques. The tutorial also discusses the behavior of square root functions and the limits of arctangent and exponential functions, providing a comprehensive understanding of these calculus concepts.

What is the limit of 1/x as x approaches positive infinity?

• 0

• Infinity

• 1

• Negative Infinity

How does the graph of 1/x behave as x approaches zero from the right?

• Approaches zero

• Approaches positive infinity

• Approaches negative infinity

• Remains constant

What is the limit of 1/x^2 as x approaches infinity?

• Negative Infinity

• Infinity

• 0

• 1

When the degree of the numerator and denominator are equal, how do you find the limit?

• Add the coefficients

• Subtract the exponents

• Multiply the terms

• Divide the coefficients

What is the limit of (8x-5)/(2x+3) as x approaches infinity?

• 0

• Infinity

• 4

• 2

How do you simplify the limit of a function involving a square root, like sqrt(16x^2 - 8)/(2x - 5)?

• Add a constant

• Divide by the highest power of x

• Multiply by the conjugate

• Use direct substitution

What is the limit of the square root of (9x^6 - x^2)/(3x^3 + 1) as x approaches infinity?

• 0

• Infinity

• 3

• 1

What is the limit of arctan(x) as x approaches infinity?

• Infinity

• Pi

• Pi/2

• 0

What is the limit of e^(-x) as x approaches infinity?

• 1

• Negative Infinity

• 0

• Infinity

What is the limit of e^x as x approaches negative infinity?

• Negative Infinity

• 1

• 0

• Infinity