limx →∞ x^x { Ans. ∞}

Name: Problem 43, Chapter 2: Mathematics for IIT JEE Main and Advanced Differential Calculus Algebra Trigonometry
Uploaded: 2021-09-06T13:09:16-08:00
Duration: 2 min 29 s
Channel: Anurag Kumar
Description: limx →∞ x^x { Ans. ∞}

step 1 In discussion we have to find the limit of defined analytical function limit x tends to infinity

Question

$$ \lim _{x \rightarrow \infty} x^{x} \quad\{\text { Ans. } \infty\} $$

   $$
\lim _{x \rightarrow \infty} x^{x} \quad\{\text { Ans. } \infty\}
$$

Mathematics for IIT JEE Main and Advanced Differential Calculus Algebra Trigonometry

Sanjiva Dayal IIT… 1st Edition

Chapter 2, Problem 43

Instant Answer

Solved by Expert Anurag Kumar

09/06/2021

Step 1

We can rewrite this function in terms of natural logarithm to simplify the calculation. Let $L = \lim_{x \rightarrow \infty} x^x$ and take the natural logarithm of both sides to get $\ln(L) = \lim_{x \rightarrow \infty} \ln(x^x)$. Show more…

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$$ \lim _{x \rightarrow \infty} x^{x} \quad\{\text { Ans. } \infty\} $$

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Key Concepts

Exponential Form Transformation

Transforming expressions into an exponential form, such as rewriting x^x as exp(x ln x), is a common technique in calculus. This method simplifies the analysis of limits and growth behavior by leveraging the properties of logarithms and exponential functions.

Exponential Growth

Exponential growth describes processes that increase at rates proportional to the current value, leading to rapid escalation. The function x^x is an example of super-exponential growth because both the base and the exponent increase, resulting in a rate of increase that outpaces standard exponential functions.

Limit at Infinity

This concept involves evaluating the behavior of a function as its variable approaches infinity. In calculus, limits at infinity help us understand the end behavior of functions and determine whether they tend to a finite value, grow without bound, or oscillate.

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