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Show that underset(nrarroo)"lim"(a.e^(x)...

Show that `underset(nrarroo)"lim"(a.e^(x)+b.e^(-x))/(c.e^(x)+d.e^(-x))=(b)/(d)[2ltelt3,dne0].`

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CHHAYA PUBLICATION-LIMIT-EXERCISE 2 ( Long Answer Type Questions)
  1. Find the values of the follwing limts : underset(nrarroo)"lim"(1.2+2...

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  2. prove the underset(nrarroo)"lim"(a.e^(x)+b.e^(-x))/(c.e^(x)+d.e^(-x))=...

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  3. Show that underset(nrarroo)"lim"(a.e^(x)+b.e^(-x))/(c.e^(x)+d.e^(-x))=...

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  4. Do the following limits exist ? underset(xrarrpi)"lim"(1)/(pi-x)

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  5. Do the following limits exist ? underset(xrarr0)"lim""Xcos"(1)/(x)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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