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Prove that the function f(x)=x^n is con...

Prove that the function `f(x)=x^n` is continuous at x=n, where n is a positive integer.

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V PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. Examine the continuity of the function f(x)=2x^2-1 at x=3

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  2. Examine the following functions for continuity f(x)=1/(x-5)

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  3. Prove that the function f(x)=x^n is continuous at x=n, where n is a p...

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  4. Is the function f defined by f(x)={(x","ifxle1),(5"," ifx>1):} continu...

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  5. Find all points of discontinuity of f where f is defined by f(x)={(2x+...

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  6. Find all points of discontinuity of f, where f is defined by f(x)={(|...

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  7. Evalute lim(xrarr0)f(x) , where f(x)={(absx/x, x ne 0),(0,x=0):}

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  8. Find all points of discontinuity of f, where f is defined by f(x)={(x/...

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

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

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

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

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

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

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

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

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

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

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

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

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