The value of lim x → 0 x a [ b x ] is, ( [ . ] → G . I . F ) Options: A . &nbsp0 B . &nbsp∞ C . &nbspba D . &nbspdoes not exist

Answer: Option C : C lim x → 0 x a [ b x ] = lim x → 0 x a ( b x − { b x } ) Since { b x } ϵ [ 0 , 1 ) = lim x → 0 x a . { b x } = 0 lim x → 0 x a [ b x ] = lim x → 0 ( x a ) ( b x ) = lim x → 0 . b a = b a

The value of limx→0xa[bx] is, ([.]→G.I.F)

Question

The value of

lim x \to 0 \frac{x}{a} [\frac{b}{x}]

is,

([.] \to G . I . F)

Options:

A . 0

B . ∞

C . ba

D . does not exist

Answer: Option C
:
C

lim x \to 0 \frac{x}{a} [\frac{b}{x}]

= lim x \to 0 \frac{x}{a} (\frac{b}{x} - {\frac{b}{x}})

Since

{\frac{b}{x}} ϵ [0, 1)

= lim x \to 0 \frac{x}{a} . {\frac{b}{x}} = 0

lim x \to 0 \frac{x}{a} [\frac{b}{x}] = lim x \to 0 (\frac{x}{a}) (\frac{b}{x})

= lim x \to 0 . \frac{b}{a}

= \frac{b}{a}

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