Question

The function f(x)=x2 + sin x - 5, then
1. f(x) is continuous at all points
2. f(x) is discontinuous at X = Pi
3. it is discontinuous at X=Pi/2
4. none of the above​

Answer 1

Answer:

lt

f(x)=

x→π

+

lt

f(x)=f(π)

Left hand limit

x→π

−

lt

x

2

−sinx+5

Put x=π−h

x→π

−

lt

(π−h)

2

−sin(π−h)+5

x→π

−

lt

(π−h)

2

−sinh+5=π

2

−sin0+5[sin(π−x=sinx)]←IIndquad

x→π

−

lt

f(x)=π

2

+5

Right Hand limit

x→π

+

lt

x

2

−sinx+5

Put x=π+h

x→π

+

lt

(π+h)

2

−sin(π+h)+5

x→π

+

lt

(π+h)

2

+sinh+5 [sin(π+x)=sinx]←IIIquad

x→π

−

lt

=π

2

+5

If π=π

2

−sinπ+5=π

2

+5

Hence

x→π

−

lt

f(x)=

x→π

+

lt

f(x)=f(π)

So f(x) is continuous at x=π