3. (i) Let {I1, I2, I3, · · ·} be a set of nested closed intervals, that is In+1 C In for all n. Prove that ... 8. n In # Ø i=1 (ii) Show that the above result need not hold if each In is allowed to be an open interval. (iii) Let {I1, I2, · , In} be a set of n intervals for some n > 3. Assume that they are pairwise intersecting, that is I; nI; # Ø for all i # j. Show using induction that n i=1 Does this contradict (ii) ? Justify your answer.

Q: Problem 2. Find all triples of integers (x, y, z) that satisfy r² + 2y? = z2.

A: (x,y,z)=(k|b2−2a2|,k(2ab),k(b2+2a2)),a,b,k∈Z+

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A: First break into partial form then use in verse laplace

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A:

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A:

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A: From the given problem:   I=∫csc-1xx3-x2dx   So we can also write as:   I=∫--2csc-1x·12x-1xdx.....1…

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A:

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A:

Q: (s-1) (s+3)(s²+2s+2) Find L-1

A: To find:-

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A:

Q: Hello can you tell me how you know that for problem 2.2 it is defined at x>5? Thanks!

A:

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Q: Problem 3. (4) 201

A:

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A: Given,         Three consecutive integers have a sum of 48.

Q: can you help me find x for these 4 problems 22=18x+4 25+8x=1 X/5+4=6 5/2+X/2=4

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Q: [1 2 31 If A = 1 2 4 find A-1 li 3 4]

A: We find inverse of Matrix A by cofactor method

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A: Let A=abcdefghidetA=2

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A: Solution: The objective is to find the derivative of the given function

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A: Topic = Integration   Formula used∫x dx = xn+1n+1+C

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A: Substitute, x2 + 2 = t.

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A: Solve using matrices addition and subtraction