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Prove : underset(xrarr0)"lim"(p^(x)-q^(x...

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

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CHHAYA PUBLICATION-LIMIT-EXERCISE 2 ( Short Answer Type Questions)
  1. Prove :underset(xrarr1)"lim"(logx)/(x-1)=1

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

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

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

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

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

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

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  8. Prove :underset(xrarr0)"lim"(log(1+sinx))/(x)=1

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  9. Prove :underset(xrarr0)"lim"(sqrt(1+x)-1)/(log(1+x))=(1)/(2)

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  10. Evaluate : underset(xrarr0)"lim"(sinx)/(log(e)(1+x)^(1/2))

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

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  12. Evaluate : underset(xrarr0)"lim"((e^(x)-1)log(1+x))/(sinx)

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  13. Evaluate : underset(xrarr4)"lim"(x^(7//2)-4^(7//2))/(log(e)(x-3))

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  14. Evaluate : underset(xrarr0)"lim"(log(1+alphax))/(sinbetax)

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  15. Evaluate : underset(xrarr0)"lim"(e^(3x)-1)/(log(1+5x))

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  16. Evaluate : underset(xrarr0)"lim"(2^(3x)-1)/(3^(2x)-1)

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  17. Find the limit (iF exists ) : underset(xrarr0)"lim"(|x|)/(x)

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  18. Find the limit *when it exists ) : underset(xrarr0)"lim"(sin|x|)/(x)

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  19. The value of [lim(x to 0)((sinx)/(x))^(sinx/(x-sinx))+lim(x to 1)x^(1/...

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  20. Find the limit (if exists ) : underset(xrarr0)"lim"(sin{x})/({x}), ( ...

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