wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The angle at which the curve y=aeax intersects the y-axis is


A

tan-1a2

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

sin-111+a4

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

cot-1a2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D

sin-11+a4

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C

cot-1a2


Find angle at which the curvey=aeax intersects the y-axis

Consider the curve y=aeax

Slope of the tangent is expressed as m=dydx

Then,

m=a2eaxm=a2Atx=0

The curve intersects y-axis at 0,a.

Consider,

m1=a2m2=

Let θ be an angle of two curve

tanθ=m1-m21+m1m2

Rewrite the above Equation as,

tanθ=m1m2-11m2+m1tanθ=a2-11+a2tanθ=-1a2tanθ=1a2θ=tan-1-1a2θ=cot-1a2

Hence, the correct answer is Option C.


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Angle between Two Planes
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon