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Putting x=theta-(pi)/(4)" prove that "un...

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

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

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

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

Prove that: (1+sintheta-costheta)/(1+sintheta+costheta)=tan(theta/2)

Prove that (1+sintheta-costheta)/(1+sintheta+costheta)="tan"theta/2 .

int_(0)^(pi)(sin4theta)/(sintheta)d theta=0

Evaluate : underset(x rarr (pi)/(4))lim (1-tan x)/(x-(pi)/(4))

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CHHAYA PUBLICATION-LIMIT-EXERCISE 2 ( Long Answer Type Questions)
  1. Do the following limits exist ? underset(xrarr0)"lim""Xcos"(1)/(x)

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  2. Does underset(xrarr4)"lim"sqrt(4-x) exist ?

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  3. Does underset(xrarr4)"lim"sqrt(4-x) exist ?

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  4. Prove : underset(xrarr0)"lim""xcos"(1)/(x)=0

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  5. Prove : underset(xrarr0)"lim"x^(2)"sin"(1)/(x)=0

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  6. Prove : underset(xrarr0)"lim"(x^(2)sin^(1/x))=0

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  7. Prove : underset(xrarroo)"lim"(sinx)/(x)=0

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  8. Prove : underset(xrarroo)"lim"(cosx)/(x)=0

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

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  10. Putting x=theta-(pi)/(4)" prove that "underset(thetararr(pi)/(4))"lim"...

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  11. A function f (x) is defined as follwos : f(x){:(=1,","" when " xne0...

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  12. Prove : underset(xrarr1)"lim"(4^(x)-4)/(x-1)=8log(e)2

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  13. Prove : underset(xrarr2)"lim"(log(2x-3))/(2(x-2))=1

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  14. If underset(xrarr0)"lim"(1+x)^(1//x)=e , show that underset(xrarr0...

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  15. If underset(xrarr0)"lim"(1+x)^(1//x)=e , show that underset(xrarr0...

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  16. If underset(xrarr0)"lim"(1+x)^(1//x)=e , show that underset(xrarr1...

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  17. If underset(xrarr0)"lim"(1+x)^(1//x)=e , show that underset(xrarr0...

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  18. If f(x)=underset(nrarroo)"lim"(1)/(1+nsin^(2)pix) , find f (x) for all...

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  19. Prove : underset(xrarroo)"lim"(sinx)/(x)=0

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  20. Evaluate the following limits : underset(x to 0) lim (e^(px)-e^(-qx)...

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