Question

lim. ( 1x ^2 +x+1/x+1)-ax-b=4
X tends to infinity
then a is
​

Answer 1

Answer:

lim

x→∞

(

x+1

x

2

+x+1

−ax−b)=4

⇒lim

x→∞

(

x+1

x(x+1)+1

−ax−b)=4

⇒lim

x→∞

(x+

x+1

1

−ax−b)=4

⇒lim

x→∞

(x(1−a)+

x+1

1

−b)=4

As the limit is infinite hence its coefficient of x=0

⇒1−a=0 or a=1

⇒lim

x→∞

⎝

⎜

⎜

⎜

⎛

x(1+

x

1

)

1

−b

⎠

⎟

⎟

⎟

⎞

=4 since lim

x→∞

x

1

=0

⇒−b=4 or b=−4

∴a=1,b=−4