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Preeti Dabral 2 years, 3 months ago
For the number 4n to end with digit zero for any natural number n, it should be divisible by 5. This means that the prime factorisation of 4 n should contain the prime number 5.But it is not possible because 4n =(2) 2n so 2 is the only prime in the factorisation of 4n . Since 5 is not present in the prime factorization, so there is no natural number n for which 4n ends with the digit zero.
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Putx+y=tdydx=dtdx−1dtdx−1=sectdtdx=sect+1∫dtsect+1=∫dx∫costdt1+costdt=x∫1+costdt−11+costdt=x∫(dt−11+cost)dt=x
t−12∫sec2t2dt=xt−tant2=x+Cx+y−tan(x+y2)=x+Cy−tan(x+y2)=C
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Ayush Kumar 2 years, 3 months ago
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