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If (x-a)^(2) + (y-b)^(2) = c^(2), for so...

If `(x-a)^(2) + (y-b)^(2) = c^(2)`, for some `c gt 0`, prove that `([1 + ((dy)/(dx))^(2)]^((3)/(2)))/((d^(2)y)/(dx^(2)))` is a constant independent of a and b.

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KUMAR PRAKASHAN-CONTINUITY AND DIFFERENTIABILITY-Miscellaneous Exercise - 5
  1. Find (dy)/(dx), If y= sin^(-1) x + sin^(-1) sqrt(1 -x^(2)), 0 le x le ...

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  2. If xsqrt(1+y+)ysqrt(1+x)=0 then (dy)/(dx) equals.

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  3. If (x-a)^(2) + (y-b)^(2) = c^(2), for some c gt 0, prove that ([1 + ((...

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  4. If cos y= x cos (a + y), with cos a ne +- 1, prove that (dy)/(dx) = (c...

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  5. If x=a (cos t+ t sin t) and y= a (sin t - t cos t), find (d^(2)y)/(dx^...

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  6. If f(x) = |x|^(3), show that f''(x) exists for all real x and find it

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  7. Using mathematical induction prove that (d)/(dx) (x^(n))= n x^(n-1) fo...

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  8. Using the fact that sin (A +B) = sin A.cos B+ cos A sin B and the diff...

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  9. Does there exist a function which is continuous everywhere but not dif...

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  10. If y= |(f(x),g(x),h(x)),(l,m,n),(a,b,c)|, prove that (dy)/(dx)= |(f'(x...

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  11. If y = e^(a cos^(-1)x) show that (1-x^(2)) (d^(2)y)/(dx^(2))-x (dy)/(d...

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  12. Differentiate w.r.t x the function (3x^(2)-9x + 5)^(9)

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  13. Differentiate w.r.t x the function sin^(3) x + cos^(6)x

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  14. Differentiate w.r.t x the function (5x)^(3 cos 2x)

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  15. Differentiate w.r.t x the function sin^(-1) (x sqrtx), where 0 le x le...

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  16. Differentiate w.r.t x the function ("cos"^(-1) (x)/(2))/(sqrt(2x + 7))...

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  17. Differentiate w.r.t x the function 0 lt x lt (pi)/(2), cot^(-1) [(sqrt...

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  18. Differentiate w.r.t x the function (log x)^(log x), x gt 1

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  19. Differentiate w.r.t x the function cos (a cos x + b sin x), for some c...

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  20. Differentiate w.r.t x the function (pi)/(4) lt x lt (3pi)/(4), (sin x ...

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