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Question

A function f(x) is defined as

f(x)=3x+4x<04x=046xx>0

then at x = 0 for f(x)

A
Limit does not exists
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B
Limit exists but discontinous
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C
Limit exists and is continuous
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D
Is not defined
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Solution

The correct option is B Limit exists but discontinous
For limit to exist, LHL = RHL

Now,

RHL limx0+f(x)=46x=4

LHL limx0f(x)=3x+4=4

Limit exists

Now for continuity,

LHL = RHL = Functional value
At x = 0
f(x)=4RHL

Discontinous

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