what is the measure of the acute angle between the curves f(x)=e-e²,g(x)=lnx and their point of intersection
option a 75 °
option b 65.2°
option c 60.5°
option d 45°
question of maths
Answers
Answered by
1
Explanation:
The given curves are y=∣x
2
−1∣ and y=
7−x
2
To find the point of intersection, let us equate both the curves.
∣x
2
−1∣=
7−x
2
Squaring on both sides gives us x
4
−x
2
−6=0
(x
2
−3)(x
2
+2)=0
On solving above quadratic equation, we get x
2
=3
The point of intersection is (±
3
,2)
The slope of the tangent to y=∣x
2
−1∣ at the point (
3
,2)is
m
1
=
dx
dy
=2x=2
3
The slope of tangent to y=
7−x
2
at the point (
3
,2)is
m
2
=
dx
dy
=
7−x
2
−x
=
2
−
3
Let θ be the acute angle between the two tangents.
tanθ=
1+m
1
m
2
m
1
−m
2
⇒tanθ=
4
−5
3
∴The tangent of the acute angle between the curves is
4
5
3
.
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