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If $\lim_{x\rightarrow 1}\frac{x^{2}-ax+b}{x-1}=5$ , then a+b is equal to :
Option 1)
-4
Option 2)
5
Option 3)
-7
Option 4)
1

Answers (1)

V Vakul

$\lim_{x\rightarrow 1}\frac{x^{2}-ax+b}{x-1}=5$

As $x\rightarrow 1$ denominator will become 0

=> for finite limit numerator must also approach to zero as $x\rightarrow 1$ .

So, L' Hospital Law will be applicable.

1-a+b=0........................(1)

Now,

$\lim_{x\rightarrow 1}\frac{x^{2}-ax+b}{x-1}=\frac{0}{0}form$

$\lim_{x\rightarrow 1}\frac{{2}x-a}{1}=5$

$2-a=5$ $=> a=-3$

and

$b=a-1$ $=>b=-3-1=-4$

So,

$a+b=-3-4=-7$

option(3) is correct.

Option 1)

-4

Option 2)

5

Option 3)
-7
Option 4)

1

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