Share
Explore BrainMass

Finding limits using Squeeze theorem and L' Hospital theorem

1. Compute the following limit: lim (x->2) [sqrt(6-x) - 2]/[sqrt(3-x) - 1]

2. Prove using the squeeze theorem lim (x->0) x^4 cos(2/x ) = 0

3. Show by means of an example that lim x-> a (f(x) + g(x)) may exist even though neither

lim x-> a f(x) nor lim x-> a g(x) exists

4. Show by means of an example that lim x-> a (f(x)g(x)) may exist even though neither

lim x-> a f(x) nor lim x-> a g(x) exists

See attached file for full problem description.

Attachments

Solution Preview

Please see the attached file to view the complete solution.

Thank you for using Brainmass.

===============================================

1. Compute the following limit:

= 0/0 when x = 2. Hence one can use L'Hospital's theorem.

Differentiating denominator and the numerator,

= = = 1/2

2. Prove using the squeeze theorem X cos( ) = 0

Values of cosine is always between -1 and +1. Hence one can ...

Solution Summary

Four questions on finding the limits of functions have been answered. Some questions require the use of well-known theorems in Calculus such as 'Squeeze theorem' and La' Hospital theorem'.

$2.19