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HIMALAYA PUBLICATION-LIMITS, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
- lim(x rarr 0) (sqrt (1+x^(2)) - sqrt(1-x^(2)))/x =
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- lim(x rarr 0) (sqrt (9+x) - sqrt(9-x))/x =
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- lim(x rarr 0) x/(sqrt (4-x) - sqrt(4+x)) =
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- lim(x rarr 0) (sqrt (3+x) - sqrt(3-x))/x =
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- lim(x rarr 2) (x^(5) sqrtx - 32 sqrt2)/(x^(3) sqrtx - 8 sqrt2) =
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- lim(h rarr 0) (sin sqrt(x+h) -sin sqrtx)/h =
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- lim(x rarr tan^(-1)) (tan^(2)x - 2tanx -3)/(tan^(2)x - 4tan x +3 ) =
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- lim(x rarr pi/3) (sin (pi/3-x))/(2 cos x-1) =
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- lim(x rarr 1) (log(e)x)/(x-1) equals :
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- lim(theta rarr 0) (sin 3 theta . sin 4 theta)/(theta . sin 5 theta) =
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- lim(x rarr 0) (sin^(3) 2x . tan^(3) 3x)/(x. (sin^(-1) 4x)^(4)) =
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- lim(x rarr 0) (1-cos nx)/(x. (1-cos mx)) =
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- lim(x rarr 0) (tan mx)/( tan nx) =
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- lim(x rarr 0) ((sin^(-1)3x)^(3) . tan x)/((tan^(-1)x)^(2).x^(2)) =
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- lim(x rarr 0) (tan^(-1)3x-4tanx)/(4 sin^(-1) 2x -7x) =
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- lim(x rarr 0) (tan^(-1)7x)/(sin 4x) =
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- lim(x rarr 0) (sin(4x)/(5x) )=
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- lim(x rarr 0) (sin^(2)(x/4))/(x^(2)) =
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- lim(x rarr 0) (1-cos 4x)/(x2) =
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- lim(x rarr 0) (1-cos 4x)/(x2) =
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