Prove that for any bounded sequences (xn) and yn we have lim sup(xn + Yn) < lim sup(xn) + lim sup(yn). Give an example that shows that equality may not hold. What is the corresponding inequality for lim inf?

Q: eax lim x → 0 In(1+ bx) -ах e

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Q: 6. a) State why the limit of f(x) = √5x - 1 does not exist for x

A: Please refer to the image below

Q: 1/x a* + b* +c* Evaluate the following limits (i) lim 3

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Q: Find lim (a + 2ar + 3ar² + n→∞ .. +nar"-¹) where |r|< 1.

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Q: х2—1 lim х-1+ In(x)

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Q: 3* –1 lim V1+x -1,

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Q: Find lim *2 x -2 In(x- 1) by using the La'Hospital Rule.

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Q: 2) Evaluate Lim X + 2² (X, Y, Z) (0, 0, 0) + Z 1 or show that it exists NOT.

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Q: Find the limit of lim x(√64x²5 ∞0++* √64x²14) = = lim x(√64x²5 -5-√√64x²-14) ∞0++x

A: limx→∞x64x2-5-64x2-14

Q: x+6x tq 4) lim X→-3 x+3

A: Given, limx→-3x2+6x+9x+3 when x tends to -3 then the given function takes the form 00, which is…