If $\lim _{\mathrm{x} \rightarrow 1} \frac{\mathrm{x}^{2}-\mathrm{ax}+\mathrm{b}}{\mathrm{x}-1}=5$, then $\mathrm{a}+\mathrm{b}$ is equal to

JEE Main · 2019 · 10 Apr 2019 · Shift 2 · Limits

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

, then

a + b

is equal to

Answer: (D)

For

x \to 1 lim \frac{x ^{2} - a x + b}{x - 1} = 5

to be finite, the zero of the denominator at

x = 1

must be cancelled, so the numerator must also vanish there:

1 - a + b = 0

, giving

b = a - 1

. Applying L'Hopital's rule,

x \to 1 lim \frac{2 x - a}{1} = 2 - a

, and this must equal

5

. Hence

a = - 3

, and then

b = a - 1 = - 4

, so

a + b = - 3 + (- 4) = - 7

JEE Main · 2019 · 10 Apr 2019 · Shift 2 · Single correct option

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