- #1
grossgermany
- 53
- 0
Homework Statement
How to rigorously (real analysis) prove that for all real c>0
Exists N such that for all n>N
ln(n)<n^c
Homework Equations
The Attempt at a Solution
The fact can be shown using graphical calculator
grossgermany said:Homework Statement
How to rigorously (real analysis) prove that for all real c>0
Exists N such that for all n>N
ln(n)<n^c
Homework Equations
The Attempt at a Solution
The fact can be shown using graphical calculator
The inequality Ln(n) This inequality is important because it shows the exponential growth of n is always greater than the logarithmic growth of n, regardless of the value of the constant c. This can have implications in fields such as biology, physics, and computer science. This inequality was first introduced by mathematician Pierre-Simon Laplace in the late 1700s, and it was later proven by mathematician Augustin-Louis Cauchy in the early 1800s. Yes, this inequality can be applied to real-world scenarios where we are dealing with quantities that grow exponentially and logarithmically, such as population growth, compound interest, and data storage. No, there are no exceptions to this inequality. It holds true for all positive values of c and for all values of n greater than or equal to 1.2. Why is this inequality important in scientific research?
3. How was this inequality discovered?
4. Can this inequality be applied to real-world scenarios?
5. Are there any exceptions to this inequality?
Similar threads
Calculus and Beyond Homework Help
Calculus and Beyond Homework Help
Calculus and Beyond Homework Help
Calculus and Beyond Homework Help
Calculus and Beyond Homework Help
Calculus and Beyond Homework Help
Calculus and Beyond Homework Help
Calculus and Beyond Homework Help
Calculus and Beyond Homework Help
Calculus and Beyond Homework Help
Share: