Math, asked by Rishav2005, 20 days ago

lim(x tens to 0) x sin 1/x is equal to (a) 0 (b) 1 (c)1/2 (d) does not exist​

Answers

Answered by debnathmanju7
0

Answer:

Correct option is A)

f(x)={

(1/x)

sin(

x

1

)

}forx

=0

⇒f(o)=0

⇒f(o

+

)f(o+h)=sin(

(o+h)

1

)=lim

h→0

(1/x)

sin(1/x)

=1

⇒f(o

)=f(o−h)=lim

h→0

(o+h)

sin

(o+h)

1

=−

h

1

sin

h

1

=1

⇒Rf

(o)=lim

h→0

h

f(o+h)−f(o)

=lim

h→0

{

sin(

o+h

1

−0)

}=lim

h→0

h

hsin1/h−0

⇒lim

h→0

sin(

h

1

),doesnotexist

f(x)iscontinuousbutnotdifferentiatable

Step-by-step explanation:

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