Series question: find 0.01^0.01

  • Thread starter Thread starter Michael_Light
  • Start date Start date
  • Tags Tags
    Series
Click For Summary
To find the value of 0.01^0.01, it is necessary to express the equation in terms of the exponential function, specifically as e^y where y = x ln(x). The discussion highlights the importance of using the exponential series and the natural logarithm to solve the problem. Participants emphasize the need to correctly identify the relationship between x and y, particularly noting that the expression should be e^(x ln(x)). The conversation indicates a collaborative effort to clarify the steps needed to arrive at the solution. Ultimately, the focus is on accurately applying mathematical principles to compute the value to three decimal places.
Michael_Light
Messages
112
Reaction score
0

Homework Statement



By expressing xx as a power of e and using the exponential series, or otherwise, find (without using tables) the value of xx when x=0.01, correct to three places of decimals. (ln10 = 2.30 to two decimal places).

Homework Equations





The Attempt at a Solution



I have tried to playing around with the exponential series and ln 10 = 2.3, but still can't get anything useful... can someone guide me?

mathematics 15.png
 
Physics news on Phys.org
Hi Michael! :smile:
Michael_Light said:
By expressing xx as a power of e

But you haven't done that …

you've written exx …

you're being asked to find y, where ey = xx :wink:​
 

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?
View full post »

Similar threads

Find the expression for the sum of this power series
  • · Replies 38 ·
2
Replies
38
Views
3K
MHB Find Sum of Series to Within 0.01
  • · Replies 6 ·
Replies
6
Views
2K
Approximating Integral via Power Series
  • · Replies 15 ·
Replies
15
Views
2K
A difficult series expansion (finding a limit)
  • · Replies 4 ·
Replies
4
Views
2K
What Is the Laurent Series for e^(1/z)?
  • · Replies 6 ·
Replies
6
Views
9K
Binomial series - Finding square root of number problem
  • · Replies 2 ·
Replies
2
Views
3K
Solving Series w/ Remainder Estimate & Integral Test
  • · Replies 2 ·
Replies
2
Views
4K
Conceptual: Are all MacLaurin Series = to their Power Series?
  • · Replies 6 ·
Replies
6
Views
3K
Help with Taylor Series problem
  • · Replies 20 ·
Replies
20
Views
12K
Fourier Series of a Piecewise Function
  • · Replies 8 ·
Replies
8
Views
4K