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Show that the function f (x) = x ^(p) si...

Show that the function `f (x) = x ^(p) sin ((1)/(x)) x , ne 0, f (0) =0` is continuous but not differentiable at ` x=0` if `0 lt p le 1.`

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The correct Answer is:
`x =0 if 0 lt p le 1`
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AAKASH SERIES-DIFFERENTIATION -SOLVED EXAMPLES
  1. Check whether the function f (x) = {{:(3 + x if x ge 0), ( 3-x if x lt...

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  2. Show that the function f (x) = {{:( x , if x lt 1), ( 3-x , if 1 le x ...

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  3. Show that the function f (x) = {{:((x -1 ) sin ((1)/(x -1)) "for" x ...

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  4. Show that the function f (x) = x ^(p) sin ((1)/(x)) x , ne 0, f (0) =0...

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  5. f(x) = x [(e^(1//x) - e^(-1//x))/(e^(1//x) + e^(-1//x))] , (x ne 0)= 0...

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  6. Find the derivativ of the function w.r.to x sin ^-1 (e ^(x) )

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  7. Find the derivativ of the function w.r.to x tan ^(-1) (e ^(x) +1)

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  8. Find the derivativ of the function w.r.to x cot ^(-1) (sin x )

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  9. Find the derivativ of the function w.r.to x cos [tan ^(-1) (log x)]

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  10. Diferentiate sin ^(-1) sqrtx w.r.t.x.

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  11. Find the derivatives of the function (cot ^(-1) x ^(3)) ^(2)

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  12. If y = sin ^(-1) ((b + a sin x )/( a +b sin x )) (a ge 0, b gt 0)

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  13. if y = Tan^(-1)(sec x + tanx) then (dy)/(dx) =

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  14. If y = x ^(x) (x gt 0) , find (dy)/(dx)

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  15. Find (d )/(dx) [(log x) ^( tan x) ].

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  16. Find the derivative dy/dx of the function y=((1-2x)^(2//3)(1+3x)^(-3//...

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  17. If y = (ax +b )/( ex +d) (ad - bcne 0) show that (ax + by) y (2) + 2 e...

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  18. If ax ^(2) + 2hxy + by ^(2) =1 then (hx + by) ^(3) y (2) =

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  19. If x =a ( t - sint ) , y =a ( 1 + cos t ) find (d ^(2) y )/(dx ^(2))...

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  20. If y = ae ^(- bx) cos (cx -d ) show that y (1) + 2 by (1) + (b^(2) ...

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