Finding limits using Squeeze theorem and L' Hospital theorem
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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
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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'.
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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 ...
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