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Prove : underset(xrarry)"lim"(cos^(2)...

Prove :
`underset(xrarry)"lim"(cos^(2)x-cos^(2)y)/(x^(2)-y^(2))=-(sin2y)/(2y)`

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CHHAYA PUBLICATION-LIMIT-EXERCISE 2 ( Short Answer Type Questions)
  1. Prove : underset(xrarr0)"lim"(sin6x+sin8x)/(sin4x+sin6x)=(7)/(5)

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

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

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

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

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

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

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

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  9. Prove : underset(xrarr0)"lim"(tan2x-x)/(3x-sinx)=(1)/(2)

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  10. Evaluate : underset(xrarr0)"lim"(e^((x+h)^(2))-e^(x^2))/(h)

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  11. Evaluate : underset(xrarr0)"lim"(e^(2x)-1)/(sin3x)

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  12. Evaluate : underset(xrarr0)"lim"(4^(x)-1)/(sin2x)

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  13. Evaluate : underset(hrarr0)"lim"(e^(2h)-1)/(e^(3h)-1)

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  14. Evaluate : underset(xrarr0)"lim"(a^(alphax)-b^(betax))/(x)

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  15. Evaluate : underset(xrarr0)"lim"(log(1+3x))/(x)

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  16. Evaluate : underset(xrarr0)"lim"(2^(x)-1)/(sqrt(1+x)-1)

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  17. Evaluate : underset(xrarr0)"lim"(e^(x)+e^(-x)-2)/(x^(2))

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  18. Prove :underset(xrarr0)"lim"(log(1+2x))/(sin3x)=(2)/(3)

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  19. Prove :underset(xrarr1)"lim"(logx)/(x-1)=1

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  20. Prove : underset(xrarre)"lim"(logx-1)/(x-e)=(1)/(e)

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