JEE MATHEMATICS MCQ: LIMITS

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Analyzing +4 | -1

Let

f(x)=\frac{x-\{x+1\}}{x-\{x+2\}}

; where

\{x\}

is the fractional part of

x

, then

\lim _{x \rightarrow 1 / 3} f(x)

View answer and explanation

Correct option: B

has value 1

Option B (has value 1) is correct because as x approaches 1/3, both the numerator and denominator of the function approach zero, and after simplification, the limit equals 1.

More Questions from LIMITS

Practice All Chapter MCQs →

\lim \limits_{{x \rightarrow 0}}\left(\frac{1}{x^2}-\operatorname{cosec}^2 x\right)

is equal to

\lim _{x \rightarrow \frac{\pi}{2}} \frac{\cos x}{(1-\sin x)^{2 / 3}}=

The value of

\lim\limits_{h \to 0} 2\left\{ {\frac{{\sqrt 3 \sin \left( {\frac{\pi }{6} + h} \right) - \cos \left( {\frac{\pi }{6} + h} \right)}}{{\sqrt 3 h\left( {\sqrt 3 \cos \,h - \sin \,h} \right)}}} \right\}

\lim \limits_{{x \rightarrow \infty}} x\left(e^{1 / x}-1\right)

is equal to If

f(x)=\frac{(x+1)^7 \sqrt{1+x^2}}{\left(x^2-x+1\right)^6}

, then the value of

f^{\prime}(0)

is equal to

\lim\limits_{n \to \infty } {\left( {1 + \sin \frac{a}{n}} \right)^n}

equals