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Prove : underset(thetararr(pi)/(4))"l...

Prove :
`underset(thetararr(pi)/(4))"lim"(2-"cosec"^(2)theta)/(1-cottheta)=2`

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

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

Putting x=theta-(pi)/(4)" prove that "underset(thetararr(pi)/(4))"lim"(sintheta-costheta)/(theta-(pi)/(4))=sqrt(2).

underset(xrarr(pi)/(2))"lim"(cosx)/((pi)/(2)-x) =

Evaluate : underset(xrarr(pi)/(2))"lim"((pi)/(2)-x)tanx

Evaluate : underset(xrarrpi)"lim"(1+cosx)/(x-pi)^(2)

Prove : underset(xrarr0)"lim"(1-cosxsqrt(cos2x))/(x^(2))=(3)/(2)

Putting z=x-(pi)/(4)" show that "underset(xrarr(pi)/(4))"lim"(1-tanx)/(1-sqrt(2)sinx)=2.

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

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CHHAYA PUBLICATION-LIMIT-EXERCISE 2 ( Short Answer Type Questions)
  1. Prove : underset(xrarr0)"lim"(tanx-sinx)/(1-cosx)=0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. Prove : underset(xrarr0)"lim"(p^(x)-q^(x))/(tanx)="log"(q)/(q)

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  17. Prove :underset(xrarr0)"lim"(sinlog(1+x))/(x)=1

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  18. Prove :underset(xrarr0)"lim"(sinlog(1+x))/(e^(x)-1)=1

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  19. Prove :underset(xrarr0)"lim"(logcosx)/(sin^(2)x)=-(1)/(2)

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  20. Prove :underset(hrarr0)"lim"(log(x+h)-logx)/(h)=(1)/(x)

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