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Maths-

General

Easy

Question

$Lt subscript x not stretchy rightwards arrow straight infinity end subscript open square brackets square root of x squared plus a x plus b end root minus x close square brackets$

a
2a
1
$\frac{a}{2}$

hint Hint:

In the question we will first rationalize the equation then we will simplify and at last put the value.

The correct answer is: $a over 2$

$Lt subscript x not stretchy rightwards arrow straight infinity end subscript open square brackets square root of x squared plus a x plus b end root minus x close square brackets equals Lt subscript x not stretchy rightwards arrow straight infinity end subscript fraction numerator open square brackets square root of x squared plus a x plus b end root minus x close square brackets open square brackets square root of x squared plus a x plus b end root plus x close square brackets over denominator open square brackets square root of x squared plus a x plus b end root plus x close square brackets end fraction equals Lt subscript x not stretchy rightwards arrow straight infinity end subscript fraction numerator x squared plus a x plus b minus x squared over denominator open square brackets square root of x squared plus a x plus b end root plus x close square brackets end fraction equals Lt subscript x not stretchy rightwards arrow straight infinity end subscript fraction numerator a x plus b over denominator open square brackets square root of x squared plus a x plus b end root plus x close square brackets end fraction d i v i d i n g space t h e space n u m e r a t o r space a n d space d e n o m i n a t o r space b y space x comma equals Lt subscript x not stretchy rightwards arrow straight infinity end subscript fraction numerator a plus begin display style b over x end style over denominator open square brackets square root of 1 plus begin display style a over x end style plus begin display style b over x squared end style end root plus 1 close square brackets end fraction equals fraction numerator a over denominator square root of 1 plus 1 end fraction equals a over 2$

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