Question

2. Evaluate the following:
1) limx ∞ √x^2+x+1 - √x^2+1

Answer 1

Answer:

y=sinx−cosx

or

2

y

=

2

1

sinx−

2

1

cosx

or

2

y

=sin(x−

4

π

). For real solution

−1≤(x−

4

π

)≤1 or −1≤

2

y

≤1

If y=1, then sinx−cosx=1

or

2

1

=sin(x−

4

π

)=sin

4

π

∴x−

4

π

=nπ+(−1)

n

4

π

n even, x=2rπ+

2

π

; n odd, x=(2r+1)π

∴x=π/2,π as 0<x<2π.