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Evaluate the following limits : under...

Evaluate the following limits :
`underset(xrarr0)"lim"(cosx-secx)/(x^(2))`

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CHHAYA PUBLICATION-LIMIT-EXERCISE 2 ( Short Answer Type Questions)
  1. Evaluate the following limits : underset(xrarr0)"lim"(2sinx-sin2x)/...

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  2. Evaluate the following limits : underset(xrarra)"lim"(1-cos(x-a))/(...

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  3. Evaluate the following limits : underset(xrarr0)"lim"(cosx-secx)/(x...

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  4. Evaluate the following limits : underset(xrarr0)"lim"(1-cos4x)/(1-c...

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  5. Evaluate the following limits : underset(xrarrpi)"lim"(1+cosx)/(pi-...

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  6. Prove : underset(xrarr0)"lim"(sinalphax^(@))/(sinbetax^(@))=(alpha)...

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  7. Prove : underset(xrarr0)"lim"((1)/(sinx)-(1)/(tanx))=0

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  8. Prove : underset(xrarr0)"lim"(tanx-sinx)/(x^(3))=(1)/(2)

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  9. Prove : underset(xrarr0)"lim"(tan^(-1)x-x)/(sin^(-1)x)=1

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  10. Prove : underset(thetararr(pi)/(4))"lim"(1-tantheta)/(1-cottheta)=-...

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  11. Prove : underset(hrarr0)"lim"(sec(x+h)-secx)/(h)=sec x tanx

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  12. Prove : underset(xrarr0)"lim"(cos9x-cos7x)/(cos7x-cos5x)=(4)/(3)

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  13. Prove : underset(xrarr0)"lim"(sin6x+sin8x)/(sin4x+sin6x)=(7)/(5)

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  14. Prove : underset(thetararr(pi)/(2))"lim"(sectheta-tantheta)=0

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  15. Prove : underset(xrarry)"lim"(cos^(2)x-cos^(2)y)/(x^(2)-y^(2))=-(si...

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  16. Prove : underset(xrarra)"lim"(sinx-sina)/(x-a)=cosa

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  17. Prove : underset(xrarra)"lim"(tanx-tana)/(x-a)=sec^(2)a

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  18. Prove : underset(xrarr0)"lim"(tanx-sinx)/(1-cosx)=0

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  19. Prove : underset(xrarr1)"lim"=cos((pix)/(2))/(1-x)=(pi)/(2)

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  20. Prove : underset(thetararr(pi)/(4))"lim"(2-"cosec"^(2)theta)/(1-cot...

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