1. limn→∞ (4n+5n)1/n=
2. limn→∞ ( xn + yn )/(xn - yn ) where x>y>1 is equal to
3)limx→ - ∞ {√(x2 - x + 1) - ax - b} = 0. then (a,b) is equal to
4)lim x→0 (cos(sin x) - cos x)/x4 is equal to
PLEASE SOLVE THESE WITH PROPER EXPLANATION
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UP 0 DOWN 0 1 2
2 Answers
23for first one take 5n cmmon , then (4/5)n →0 as n→∞ so limit is 5
second is similar , take xn common , y/x bcomes fraction, and (y/x)n tends to zero as n →∞
for third , rationalise first, then put y = -x , and then check wat shud be done to keep the limit finite i.e 0 here.
for fourth use the half angle formula of 1- cosx = 2sin2(x/2)
i.e 1-cos(sinx) = 2sin2((sinx)/2)
