Recognize that as approaches infinity, the term represents .
Understand that approaches 0 as approaches infinity because the denominator grows very large.
Multiply the limit of by , which is a constant, to find the limit of the entire expression.
Conclude that the limit of as approaches infinity is 0.
Recommended similar problem, with video answer:
Verified Solution
This video solution was recommended by our tutors as helpful for the problem above
Video duration:
4m
Play a video:
Was this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Limits at Infinity
Limits at infinity refer to the behavior of a function as the input approaches infinity. This concept is crucial in calculus for understanding how functions behave in extreme cases, particularly for rational functions, polynomials, and exponential functions. Evaluating limits at infinity helps determine horizontal asymptotes and the end behavior of functions.
Negative exponents indicate the reciprocal of the base raised to the corresponding positive exponent. For example, t^−5 is equivalent to 1/t^5. Understanding negative exponents is essential for simplifying expressions and evaluating limits, especially as the variable approaches infinity, where terms with negative exponents tend to zero.
The behavior of functions as t approaches infinity involves analyzing how the function's value changes as t increases without bound. In the case of polynomial functions with negative exponents, the function's value will approach zero. This concept is vital for determining the limit of functions at infinity and understanding their long-term trends.