if f(x)=⌊x^2 ⌋ and A=lim_(x→0) (f(x)−f(−x)) and B=f(x)+f(−x) when x=0 find A and B


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Question Number 85868 by M±th+et£s last updated on 25/Mar/20

$i f f (x) = ⌊ x^{2} ⌋$ $a n d A = \underset{x \to 0}{l i m} (f (x) - f (- x))$ $a n d B = f (x) + f (- x) w h e n x = 0$ $f i n d A a n d B$
Commented by mr W last updated on 25/Mar/20

$A = 0 - 0 = 0$ $B = 0 + 0 = 0$
Commented by M±th+et£s last updated on 25/Mar/20

$t h a n k y o u s i r s i r b u t w h y \underset{x \to 0}{l i m} (f (x) - f (- x)) = 0$
Commented by M±th+et£s last updated on 25/Mar/20

$s o r r y i m e a n f (x) + f (- x)$
Commented by M±th+et£s last updated on 25/Mar/20
$⌊x⌋+⌊−x⌋= { ((0 x∈z)),((−1 x∉z)) :} lim_(x→0^+ ) (−1)=−1 lim_(x→0^− ) (−1)=−1 so lim_(x→0) f(x)+f(−x)=−1$
$⌊ x ⌋ + ⌊ - x ⌋ = {\begin{cases} 0 x \in z \\ - 1 x \notin z \end{cases}$ $\underset{x \to 0^{+}}{l i m} (- 1) = - 1$ $\underset{x \to 0^{-}}{l i m} (- 1) = - 1$ $s o \underset{x \to 0}{l i m f} (x) + f (- x) = - 1$
Commented by mr W last updated on 25/Mar/20

$b u t h e r e f (x) = ⌊ x^{2} ⌋ a s y o u g a v e .$
Commented by M±th+et£s last updated on 25/Mar/20

$y o u a r e r i g h t s i r i a m s o s o r r y i t w a s a t y p o$
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