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SIA PUBLICATION-FUNCTIONS AND MATHEMATICAL INDUCTION -Problems
- If f : N to Z is defined by f(x)={{:("2 if "n = 3k" , " k ...
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- The function f:R rarrR is defined by f(x)=3^(-x). Observe the followin...
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- If n in N , and the period of (cos nx)/(sin(x//n)) is 4pi , then n=
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- If f(x)={{:([x]","if-3lt x le-1),(|x|","if-1 lt x lt 1),(|[x]|","if 1 ...
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- sum(k=1)^(5)(1^(3)+2^(3)+…+k^(3))/(1+3+5+….+(2k-1)) is equal to
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- If f:RR rarrRR and g:RR rarrRR are defined by f(x)=2x+3 and g(x)=x^(2)...
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- Suppose f:[-2, 2] rarr RR is defined by f(x)={{:(-1" for "-2 le x le 0...
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- If f : R to R and g : R to R are given by f(x)=|X| and g(x)=[x] for ea...
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- The period of the function f( theta ) = sin""(theta )/(3) + cos""(th...
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- If t(n)=(1)/(4)(n+2)(n+3) for n = 1, 2, 3,… then (1)/(t(1))+(1)/(t(2))...
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- Let A={x in R : x ne 0, -4le xle4} and f:A rarrR is defined by f(x)=(|...
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- If f(x)=(cos^(2)x+sin^(4)x)/(sin^(2)x+cos^(4)x) for x in R then f(2002...
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- The function f:R rarrR defined by f(x)=cos^(2)x+sin^(4)x" for " x in R...
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- If f:R rarr and g:R rarr R are defined by f(x)=3x-4 and g(x)=2+3x then...
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- If f(x)=sin^(2)((pi)/8 + (x)/2) -sin^2((pi)/8-(x)/(2)), then the perio...
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- If f(x)=(25-x^(4))^(1//4) for 0 lt x lt sqrt5 then f(f((1)/(2)))=
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- Define f:Z rarrZ by f(x)={{:(x//2,"(x is even)"),(0,"(x is odd)"):} th...
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- Let f: R rarrR be defined by f(x)={{:(x+2, (xle-1)),(x^(2), (-1lexle1)...
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- Two functions f:Rrarr R, g:R rarr R are defined as follows : f(x)={{...
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- If 2^(3)+4^(3)+6^(3)+….+(2n)^(3)=h n^(2)(n+1)^(2) then h is equal to
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