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If f(x)=lim(ntooo)(x^(n)g(x)+h(x))/(x^(n...

If `f(x)=lim_(ntooo)(x^(n)g(x)+h(x))/(x^(n)+1)` show that
f(x) =h(x), when `0ltxlt1`
` =(1)/(2)[h(x)+g(x)]`, when x=1
=g(x), when `xgt1`

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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-CALCULUS
  1. Show that : lim(xto0)[(1)/(x)-(log(1+x))/(x^(2))]=(1)/(2)

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  2. Show that : lim(xto(pi)/(4))(sqrt2-(sinx+cosx))/((4x-pi)^(2))=(1)/(1...

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  3. If f(x)=lim(ntooo)(x^(n)g(x)+h(x))/(x^(n)+1) show that f(x) =h(x), wh...

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  4. If lim(xto0)(sin2x+asinx)/(x^(3)) is finite, find a and the limit.

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  5. Evaluate the following limits: lim(xto0)(sqrt(x^2-1)+sqrt(x-1))/(sqr...

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  6. Evaluate the following limits: lim(xto2a)(sqrt(x-2a)+sqrtx-sqrt2a)/(...

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  7. Evaluate the following limits: lim(xto0)(sinx^(2)(1-cosx^(2)))/(x^(6...

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  8. Evaluate the following limits: lim(xto0)(xe^(x)-log(1+x))/(x^(2))

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  9. Evaluate the following limits: lim(hto0)((a+h)^(2)sin(a+h)-a^(2)sina...

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  10. Evaluate the following limits: lim(ntooo)[(n)/(n^(2))+(n+1)/(n^(2))+...

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  11. Evaluate the following limits: lim(xto3)(3-sqrt(6+x))/(3sqrt3-sqrt(6...

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  12. Evaluate the following limits: lim(xto0)(sqrt(cosx)-root3cosx)/(sin^...

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  13. Evaluate the following limits: lim(xto0)[coec^(3)xcotx-2cot^(3)xcose...

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  14. Evaluate the following limits: lim(xto(pi)/(2))(xtanx-(pi)/(2)secx)

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  15. Show that lim(xto1)(sqrt(1-cos(x-1)))/(x-1) does not exist.

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  16. Evaluate: lim(xto2)(2^(x)+2^(3-x)-6)/(sqrt(2^(-x))-2^(1-x))

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  17. Evaluate: lim(xto(pi)/(2))((2xsecx)/(pi)-tanx)

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  18. Evaluate: lim(xto0)(cosx)^(cot^(2)x)

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  19. Evaluate: lim(xto(1)/(2))(cos^(2)pix)/(e^(2x)-2ex)

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  20. Evaluate: lim(xto(pi)/(3))(tan^3x-3tanx)/(cos(x+(pi)/(6)))

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