Question

Find the angle between curves f(x) = 2' log x and
g(x) = x2x - 1.​

Answer 1

Answer:

f(x)=2

x

log

e

x,g(x)=x

2x

−1

f

1

(x)=

x

2

x

+logx.2

x

ln2 , g

1

(x)=x

2x

(2

2

1

+ln2x)

As, f(x) & g(x) meets at x=1

f

1

(1)=2(m

1

),g

1

(1)=1+ln2(m

2

)

tanθ=

1+m

1

m

2

m

1

−m

2

=

1+2(1+ln2)

2−(1+ln2)

=

3+ln2

1−ln2

⇒cosθ=0.99