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Consider f(x)=int1^x(t+1/t)dt and g(x)=f...

Consider `f(x)=int_1^x(t+1/t)dt` and `g(x)=f'(x)` If P is a point on the curve `y=g(x)` such that the tangent to this curve at P is parallel to the chord joining the point `(1/2,g(1/2))` and `(3,g(3))` of the curve then the coordinates of the point P

A

can't be found out

B

`((7)/(4),(65)/(28))`

C

`(1, 2)`

D

`(sqrt((3)/(2)),(5)/(sqrt6))`

Text Solution

Verified by Experts

The correct Answer is:
D
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ARIHANT MATHS-DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS -Exercise (Single Option Correct Type Questions)
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  4. Number of positive integral value(s) of 'a' for which the curve y=a^(x...

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  9. Water runs into an inverted conical tent at the height of the water is...

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  10. Let f(x)=x^3-3x^2+2x . If the equation f(x)=k has exactly one posit...

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  11. The x-intercept of the tangent at any arbitarary point of the curve (a...

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  12. If f(x) is continuous and differentible over [-2, 5] and -4lef'(x)le3 ...

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  13. A curve is represented parametrically by the equations x=t+e^(at) and ...

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  14. At any two points of the curve represented parametrically by x=a (2 co...

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  15. Let F(x)=int(sinx)^(cosx)e^((1+sin^(-1)(t))dt on [0,(pi)/(2)], then

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  16. Given f' (1) = 1 and d/(dx) f(2x))=f'(x) AA x > 0. If f' (x) is diff...

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  17. Let f(x)a n dg(x) be two functions which are defined and differentiabl...

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  18. The range of values of m for which the line y = mx and the curve y=(x)...

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  19. Let S be a square with sides of length x. If we approximate the change...

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  20. Consider f(x)=int1^x(t+1/t)dt and g(x)=f'(x) If P is a point on the cu...

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