R (T) is bounded by its value at the origin i.e., IR, (t)l

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Q: 3- S Srår de

A: Find range of r and theta . Here r varies from 1 to 4 and theta varies from -π/2 to +π/2

Q: . Prove that an→L = Jan] → |L]. (Make cas

A: Given that an is a sequence which converges to L that is, an→L. Then we have to prove that |an|…

Q: Prove that: cscz- cot z = 1 2. 2. %3D

A: We need to prove the identity  csc2z-cot2z=1

Q: Prove that {i} = I. ¡El

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Q: State the Fermet's Last Theorem. Who was French women mathematican who mede significant 19th century…

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Q: 5. Show that () = () +().

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Q: Show how James Garfield (1831-1881) proved Pythagorean Theorem

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Q: Prove that if gcd (a,b)=1>then gcd (ab,ab)=l

A: I have proved using the fact that gcd can be expressed as integers linear combination q

Q: How many counterexamples are needed to prove that a statement is false?

A: Suppose P(x) be the statement.

Q: State Fermat’s Theorem

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Q: 4. If X and Y are independent RVs, then O2+ ,(@) = ¢,(@) × ¢,(@)

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Q: 8. [ tan’rd.r

A: We have to find the integration of given questions.

Q: Prove that 1lellse TlI

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Q: Expend (I+x)

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Q: is R* is contractible?

A: This is a problem of Topology.

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A:

Q: Given that x, y, and z . Prove that if (x^2)|y and (y^3)|z, then (x^6)|z

A: Solution: The objective is to prove that the given statement

Q: b22 Such that/2/-1E andArg 4.

A: We find complex number

Q: 7. Theorem 94 I (9x-25)

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Q: Show that A\ (Bnc) (A\B)U(A\C).

A:

Q: Which is the most famous theorem of pierre de fermat?

A: To tell which is the most famous theorem of Pierre de fermat

Q: [2 4 21 A = l1 3 1 1 1 B = -2 -1 [2 4 D = 4 C = 1 3 21 -1 %3D 2

A: Given A = 242131B = -1111-2-1C = 242131D = 1-1-1-121 Clearly  C = AD = -B

Q: Find gcd(1000, 34) and lcm(1000, 34) and verify that gcd(1000, 34) · lcm(1000, 34) = 1000 · 34

A: 1000 can be written in the form of prime factors as 1000=2×2×2×5×5×5 34 can be written in the form…

Q: 2017 J Q3 + V5 in the form a+bV5, where a and b are integers. Without using a calculator, express -2…

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Q: .Prove that la + b + c| < |a] + |b| + ]c]

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Q: If a =(2,3,-1) ,(1,6,0) ,(2,1,3) prove that Aa^-1 =A^-1A=I Please show all the step

A: Given matrix is, A=23-1160213

Q: Prove algebraically that  A+A'B'=A+B'

A: We have to prove algebraically that  A + A'B' = A + B' We know that, the distributive property  A +…

Q: Approximate the value of In (1000!)

A: Given that ln1000!. The objective is to approximate the value. The expansion for…

Q: 1 의( (eat – ebt)} = %3D la-b (s-a)(s-b)

A: Here we have to prove that,  L1a-beat-ebt=1s-as-b

Q: w Write down the de finition of IT. 5.

A: Please go through the given definition of Pi given below,

Q: [о, 1] x [1, 2]

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Q: (49-12)3/2 +6 - dt

A: