Question

solve limit x approaches to infinity when (3^x+1)-(5^x+1 )/ (3^x)-(5^x​)​

Answer 1

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

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