Q. 45.0( 1 Vote )

# Find which of the functions is continuous or discontinuous at the indicated points:at x = 2

Given,

…(1)

We need to check its continuity at x = 2

A function f(x) is said to be continuous at x = c if,

Left hand limit(LHL at x = c) = Right hand limit(RHL at x = c) = f(c).

Mathematically we can represent it as-

Where h is a very small number very close to 0 (h0)

Now according to above theory-

f(x) is continuous at x = 2 if -

Clearly,

LHL = {using equation 1}

LHL =

LHL =

LHL =

LHL = 5 -2(0) = 5 …(2)

Similarly we proceed for RHL-

RHL = {using equation 1}

RHL =

RHL =

RHL =

RHL = 5 + 2(0) = 5 …(3)

And,

f(2) = 5 {using eqn 1} …(4)

Clearly from equation 2 , 3 and 4 we can say that

f(x) is continuous at x = 2

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