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Show that π(βπ, π) = βπΏ(π, π) and πΏ(βπ, π) = βπ(π, π).Β
Let π be differentiable. Show that if limπ₯ββ π(π₯) = πΏ β β then limπ₯ββ π β² (π₯) = 0. Provided that the latter limit is existing. Give an example where the converse is not true. Also give an example for which the limit of π β² is not existing even though the limit of π is the same as given.
Β Let π be differentiable. Show that if lim π₯ββ
π(π₯) = πΏ β β then lim π₯ββ
πβ²(π₯) = 0. Provided that the latter limit is existing. Give an example where the converse is not true. Also give an example for which the limit of πβ² is not existing even though the limit of π is the same as given.Β
Let x1 > 1 and xn+1 := 2 β
1
xn
for all n β N. Show that {xn} is bounded
and monotone. Find the limit.
SUPPOSE that f [0,2]-> R is continuous on[02] and differentiableon [0,2] and that f(0)=0 f(1)=1, f(2)=1.... show that there exits c1 belongs to (0,1) such that f (c1)=1
Determine the local minimum and local maximum values of the function f defined by f(X)=3-5x3+5x4-x5
