In: Advanced Math

state and prove Theorem Holomorphy of R**λ**

state and prove spectral mapping theorem

State and prove spectral mapping theorem

State and prove spectral mapping theorem

State and prove Lebesgue Dominated Convergence theorem.

State and prove the Generalised Mean Value Theorem.

Explain what it is a neutral theorem
in Euclidean geometry.
State & prove both: the theorem on construction of parallel
lines and its converse. Which one of them is neutral?

Question 1. State the prove The Density Theorem for Rational Numbers.
Question 2. Prove that irrational numbers are dense in the set of real numbers.
Question 3. Prove that rational numbers are countable
Question 4. Prove that real numbers are uncountable
Question 5. Prove that square root of 2 is irrational

Question 1. State the prove The Density Theorem for Rational Numbers.
Question 2. Prove that irrational numbers are dense in the set of real numbers.
Question 3. Prove that rational numbers are countable
Question 4. Prove that real numbers are uncountable
Question 5. Prove that square root of 2 is irrational

State Babinet’s theorem; and use Huygens’s principle to prove
it.

State and prove the Weighted Mean Value Theorem for
integrals.

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