Question

: Discuss the continuity of the function f(x)=xtan(1/x) at x = 0 given that x≠0 and f(0)=0.

Answer 1

Answer: 0

Step-by-step explanation: hope this helps

Answer 2

Answer:

Given,

f(x)=xtan

−1

x

1

for x



=0

and f(0)=0

∵−

2

π

≤tan

−1

x

1

≤

2

π

∴−

2

π

x≤xtan

−1

x

1

≤

2

π

x

Here,

x→0

lim

xtan

−1

x

1

=

x→0

lim

x

1

tan

−1

x

1

=0

And f(0)=0

∴ f(x) is continuous at x=0

But

x→0

lim

x−0

f(x)−f(0)

=

x→0

lim

tan

−1

x

1

does not exist

∴ f(x) is not differential at x=0

Step-by-step explanation:

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