UPSEE 2017 Solved Paper

Given,From above conditions function f(x) is continuous throughout the real line, when function f(x) is continuous at x=−

π

2

and

π

2

.
For continuity at x=−

π

2

lim

x→− π− 2

f(x)=

lim

x→− π+ 2

f(x)=f(−

π

2

) ......(ii)

lim

x→− π− 2

f(x)=2

lim

x→− π+ 2

f(x)=−A+B
f(−

π

2

)=2
∴ From Eq. (ii), we get
−A+B=2 ......(iii)
For continuity at x=π.2

lim

x→ π 2

f(x)=

lim

x→ π+ 2

f(x)=f(

π

2

) ........(iv)
Here,

lim

x→ π− 2

f(x)=A+B⇒

lim

x→ π+ 2

f(x)=0
And f(

π

2

)=0
∴ From Eq. (iv)
A+B=0 .......(v)
∴ From Eqs. (iii) and (v)
A=−1,B=1