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HIMALAYA PUBLICATION-LIMITS, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
- If f be a function such that f(9) = 9 and f'(9) = 3, then : lim(x ra...
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- lim(x rarr 0) ((1^(x)+2^(x)+3^(x)+……….+n^(x))/n)^(1/x) =
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- If f(x) = (sin (e^(x-2) - 1))/(log (x - 1)), then lim(x rarr 2) f(x) i...
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- lim(x rarr 0) ((tan x -x)/x). (Sin) 1/x =
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- If lim(x rarr 0) (x(1+m cos x)-n(sin x))/x^(3) =1 then
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- lim(x rarr 0) (cos x + a sin bx)^(1/x) =
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- lim(x rarr a) (x^(7/6)-a^(7/6))/(x^(3/5)-a^(3/5)), (a gt 0) =
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- lim(n rarr oo) [1/(1-n^(4))+ 8/(1-n^(4))+ ....+ n^(3)/(1-n^(4)]] =
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- lim(n rarr oo) [2/3 + (2/3)^(2) + (2/3)^(2)+.....+(2/3)^(n)] =
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- lim(n rarr oo) (1)/(n^(3)) sum(r = 1)^(n) r^(2) is :
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- lim(x rarr oo) (1)/(n^(4)) sum(r = 1)^(n) r^(3) is :
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- lim(n rarr oo) ((1)/(1.2) + (1)/(2.3) + (1)/(3.4) +…..+ (1)/(n(n+1))) ...
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- lim(n rarr oo) 1/n^(3) { 1+3+6+...+ (n(n+1))/2} =
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- If S(n) = (1)/(1.4)+(1)/(4.7) + (1)/(7.10) +……. to n terms, then lim(n...
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- lim(x rarr 1) (x^(2)-1)/(|x-1|) =
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- If f(x) = {(1/(1+e^(1/x)), x ne 0),(0, x= 0):} then f(x) is
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- The right hand and left hand limit of the function f(x)={{:((e^(1//x)-...
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- Let f(x) = {(x", if x is irrational"),(0", if x is ratinal"):} then f ...
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- f(x) = (x^(3)+x^(2)-16x+20)/(x-2)^2, x ne 2. The value which should be...
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- Let f(x) = (tan ((pi)/(4) - x))/(cot 2 x), x ne pi//4, the value which...
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