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If f(x)=underset(nrarroo)"lim"(1)/(1+nsi...

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

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Verified by Experts

The correct Answer is:
`f(x){:(=1,",""whenxis an integer" ),(=0,",""when x is not an integer"):}`
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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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