- #1
Miike012
- 1,009
- 0
Problem: Determine the limit l for the given a, and prove that it is the limit by showing how to find a δ such that abs(f(x) - l)< ε for all x satisfying 0< abs( x - a) < δ.
** abs = absolutue value of...
Solution:
f(x) = x(3-cos(x^2))
The limit l is zero. hence the product of some number times zero is zero.
abs(f(x) - 0)< ε = abs(x(3-cos(x^2)).
abs((3-cos(x^2))≤ 1, abs(x(3-cos(x^2))< abs(x)
Thus for every number x, If abs(x) < ε Then abs(x(3-cos(x^2)),
Which finishes the proof, concluding that the limit of f(x) near zero is zero.
** abs = absolutue value of...
Solution:
f(x) = x(3-cos(x^2))
The limit l is zero. hence the product of some number times zero is zero.
abs(f(x) - 0)< ε = abs(x(3-cos(x^2)).
abs((3-cos(x^2))≤ 1, abs(x(3-cos(x^2))< abs(x)
Thus for every number x, If abs(x) < ε Then abs(x(3-cos(x^2)),
Which finishes the proof, concluding that the limit of f(x) near zero is zero.