InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Consider f(x) = int_(1)^(x)(t + 1t)dtand g(x) = f'(x) for x in [1/2, 3].If P is a point on the curve y = g(x)such that the tangent to curve at P is parallel to a chord joining the points (1/2, g(1/2))and (3,g(3))of the curve, then if ordinate of point P is lambda then sqrt(6) lambda is equal to: |
|
Answer» `G(x)=x+(1)/(x)" for "x in [(1)/(2),3]` `g((1)/(2))=(5)/(2),g(3)=(10)/(3)` `P(alpha, g(alpha)),alpha in [(1)/(2),3]` Let `"By L.M.V.T"` `g.(alpha)=(g(3)-g((1)/(2)))/(3-(1)/(2))` `1-(1)/(alpha^(2))=((10)/(3)-(5)/(2))/((5)/(2))=(4-3)/(3)=(+1)/(3)` `alpha^(2)=(3)/(2)rArr alpha=sqrt((3)/(2))` `g(alpha)=sqrt((3)/(2))+(1)/(sqrt(3//2))` `lambda=(5)/(sqrt6)` `lambdasqrt6=5` |
|