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Examine the continuity of the function ...

Examine the continuity of the function `f(x)={(x^3-3, if ,x le 2),( x^2+1, if , xgt2):}`.

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V PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. Find all points of discontinuity of f, where f is defined by f(x)={(x/...

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  2. Examine the continuity of the function <be> f(x)={(x+1,xge1),(x^2+1,x<...

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  3. Examine the continuity of the function f(x)={(x^3-3, if ,x le 2),...

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  4. Examine whether the function defined by f(x)={(x+5,xle1),(x-5,x>1):}...

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  5. Discuss the continuity of the function f(x)={(2 x , if , xlt0),( 0,...

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  6. Find the derivative of the function given by f(x)=sin (x^2)

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  7. Differentiate the function f(x)=sin [cos x^2] with respect to x.

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  8. Differentiate the functions with respect to x: sin (x^2+5)

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  9. Differentiate the functions with respect to x: cos (sin x)

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  10. Differentiate the functions with respect to x: sin(a x+b)

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  11. Differentiate sec(tan(sqrtx)) w.r.t.x

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  12. Differentiate sin(ax+b)/(cos(cx+d)) w.r.t.x

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  13. Differentiate cos(x^3)sin^2(x^5) w.r.t.x

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  14. Differentiate the functions with respect to x: 2 sqrt(cot x^2)

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  15. Differentiate cos(sqrtx) w.r.t.x

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  16. Prove that the function f is given by f(x)=|x-1|, x in R is not differ...

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  17. Find (dy)/(dx) if x-y=pi

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  18. Find (dy)/(dx) if y+siny=cosx

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  19. Find the derivative of f given by f(x)=sin ^(-1) x assuming it exist.

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  20. Find the derivative of f given by f(x)=tan ^(-1) x assuming it exists.

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