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Using differentials, find the approximat...

Using differentials, find the approximate value of each of the following:
(a)`(17/81)^(1/4)" "(b) (33)^(-1/5)`

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AI Generated Solution

To find the approximate values of \( \left( \frac{17}{81} \right)^{1/4} \) and \( 33^{-1/5} \) using differentials, we can follow these steps: ### Part (a): Approximate \( \left( \frac{17}{81} \right)^{1/4} \) 1. **Define the function**: Let \( f(x) = x^{1/4} \). 2. **Find the derivative**: ...
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NAGEEN PRAKASHAN ENGLISH-APPLICATIONS OF DERIVATIVES-Miscellaneous Exercise
  1. Using differentials, find the approximate value of each of the follow...

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  2. Show that the function given by f(x)=(logx)/xhas maximum at x = e.

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  3. The two equal sides of an isosceles triangle with fixed base b are ...

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  4. Find the equation of the normal to the curve x^2=4\ y which passes ...

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  5. Show that the normal at any point theta to the curve x=acostheta+at...

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  6. Find the intervals in which the function f given by f(x)=(4sinx-2x-x c...

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  7. Find the intervals in which the function f given by f(x)=x^3+1/(x^3),\...

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  8. Find the area of the greatest isosceles triangle that can be inscri...

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  9. A tank with rectangular base and rectangular sides, open at the top ...

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  10. The sum of the perimeter of a circle and square is k, where k is so...

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  11. A window is in the form of a rectangle surmounted by a semicircular...

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  12. A point on the hypotenuse of a triangle is at distance a and b from...

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  13. Find the points at which the function f given by f(x)=(x-2)^4(x+1)^3 h...

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  14. Find the absolute maximum and minimum values of the function f give...

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  15. Show that the altitude of the right circular cone of maximum volume ...

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  16. Let f be a function defined on [a, b] such that f^(prime)(x)>0, for al...

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  17. Show that the height of the cylinder of maximum volume that can be ...

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  18. Show that height of the cylinder of greatest volume which can be in...

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  19. A cylindrical tank of radius 10 m is being filled with wheat at the r...

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  20. The slope of the tangent to the curve x=t^2+3t-8,y=2t^2-2t-5at the po...

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