Question

limit of x is infinity xcos[π/8x]sin [π/8x] is equal to
​

Answer 1

Step-by-step explanation:

As x→∞,cos(

8x

π

)→1

Looking at the rest of the part,

x→∞

lim

8x

π

→0

x→∞

lim

x.sin(

8x

π

)

=

x→∞

lim

x

1

sin(

8x

π

)

We multiply and divide by

8

π

=

x→∞

lim

,

8x

π

sin(

8x

π

)

×

8x

π

Now using the property of a limit,

y→0

lim

,

y

siny

=1

We get, applying the limit,

=1×

8

π

=

8

π

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