Question

Is the function defined by f (x) = x² – sin x + 5 continuous at x = π?

Answer 1

Question:-

Is the function defined by f (x) = x² – sin x + 5 continuous at x = π?

Answer:-

f(x)= x²-sin x +5

we need to check continuity at x=π

we know that

a function f is continuous at x=π

i.e. Lim f(x)= f(x)

x→π

_____________________

LHS. ___________________________

Lim f(x)

x→π

= lim (x²-sin x +5)

x→π

= (π)²-sin π +5

=π²-0+5 ( as sin π= 0)

= π²+5

_____________________

RHS

_____________________

f(x)= x²-sin x +5

f(π)= π²-sin π +5

=π²-0+5 ( as sin π= 0)

= π²+5

_____________________

thus, Lim f(x)= f(c)

x→π

f is continuous at x=π ..

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