30 points
Time management is very much important in IIT JAM. The eduncle test series for IIT JAM Mathematical Statistics helped me a lot in this portion. I am very thankful to the test series I bought from eduncle.
Nilanjan Bhowmick AIR 3, CSIR NET (Earth Science)
- IIT JAM
- Mathematics (MA)
Pls tell what mistake i am doing ...i have attached my explanation also..
pls tell what mistake i am doing ...i have attached my explanation also..
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Srj Best Answer
Given function is discontinuous everywhere except single point pi/4. see the defination of function. it is cos at rational and sin on irrational. as both rational and irrational are dense. for any number one can find atleast one rational sequence and irrational sequence converging to that point. but both sequence limit are different on that function. so discontinuous at that point. so one can show discontinuous at each point other than pi/4. As cos and sin have same value at that point. We can prove it is not Riemann integrable. proof is same as non Riemann integrability of dirichlet function. if you want proof let me know I will add proof.
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got it sir ..thanks a lot sir
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Srj
Given function is discontinuous everywhere except single point pi/4. see the defination of function. it is cos at rational and sin on irrational. as both rational and irrational are dense. for any number one can find atleast one rational sequence and irrational sequence converging to that point. but both sequence limit are different on that function. so discontinuous at that point. so one can show discontinuous at each point other than pi/4. As cos and sin have same value at that point. We can prove it is not Riemann integrable. proof is same as non Riemann integrability of dirichlet function. if you want proof let me know I will add proof.
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Srj
Given function is discontinuous everywhere except single point pi/4. see the defination of function. it is cos at rational and sin on irrational. as both rational and irrational are dense. for any number one can find atleast one rational sequence and irrational sequence converging to that point. but both sequence limit are different on that function. so discontinuous at that point. so one can show discontinuous at each point other than pi/4. As cos and sin have same value at that point. We can prove it is not Riemann integrable. proof is same as non Riemann integrability of dirichlet function. if you want proof let me know I will add proof.
-
Srj
Given function is discontinuous everywhere except single point pi/4. see the defination of function. it is cos at rational and sin on irrational. as both rational and irrational are dense. for any number one can find atleast one rational sequence and irrational sequence converging to that point. but both sequence limit are different on that function. so discontinuous at that point. so one can show discontinuous at each point other than pi/4. As cos and sin have same value at that point. We can prove it is not Riemann integrable. proof is same as non Riemann integrability of dirichlet function. if you want proof let me know I will add proof.
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