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Evaluate: ("lim")(xvec0)(tanx-sinx)/(x^3...

Evaluate: `("lim")_(xvec0)(tanx-sinx)/(x^3)`

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Evaluate lim_(xto0) (a^(tanx)-a^(sinx))/(tanx-sinx),agt0

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Which of the following limits tends to unity? (a) ("lim")_(xvec0)sin(tanx)/(sinx) (b) ("lim")_(xvecpi/2)sin(cosx)/(cosx) ("lim")_(xvec0)"sin"(e^x-1)/x (d) ("lim")_(xvec0)(sqrt(1+x)-sqrt(1-x))/x

BANSAL-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Evaluate: ("lim")(xvec0)1/xsin^(-1)((2x)/(1+x^2))

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  2. Evaluate: ("lim")(xvec0)(1-cos2x)/(x^2)

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  3. Evaluate: ("lim")(xvec0)(tanx-sinx)/(x^3)

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  4. Evaluate: lim(x->pi/2)(1+cos2x)/((pi-2x)^2)

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  5. lim {x->oo} 2^(x-1) tan(a/(2^x))

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  6. Evaluate: lim(x->2)(x^2-x-2)/(x^2-2x-"sin"(x-2))

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  7. Evaluate: lim(x->oo)x(tan^(-1)((x+1)/(x+4))-pi/4)

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  8. Evaluate: (lim)(x->0)sin8xcot3x. If it is of the form p/q, then (p+q)=...

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  9. Evaluate the following limit: (lim)(x->0)(1-cos x)/(x^2)

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  10. Evaluate the following limit: (lim)(x->0)(1-cos5x)/(3x^2)

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  11. Evaluate the following limit: (lim)(x->0)(sqrt(1+t a n x)-sqrt(1+sin...

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  12. Evaluate the following limit: (lim)(x->1)(x^3+x^2-2)/("sin"(x-1))

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  13. Evaluate the following limit: (lim)(x->1)(1-x)tan(pix)/2

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  14. Evaluate the following limit: (lim)(x->0)(xtan2x-2xtanx)/((1-cos2x)^...

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  15. lim(x->0)(cos7x-cos9x)/(cosx-cos5x)

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  16. Evaluate the following limit: (lim)(x->0)(1-cos xsqrt(cos2x))/(tan^...

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  17. Evaluate the following limit: (lim)(x->0)(1-"cos"(1-cos x))/(sin^4x...

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  18. Evaluate the following limit: (lim)(x->0)(1-cos m x)/(1-cos n x)

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  19. Evaluate the following limit: (lim)(x->pi/4)(sqrt(2)cosx-1)/(cotx-1...

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  20. Evaluate the following limit: (lim)(x->0)(cos2x-cos e c2x)/x

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