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Evaluate : underset(xrarr0)"lim"(e^(...

Evaluate :
`underset(xrarr0)"lim"(e^(alphax)+e^(betax)-2)/(x)`

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The correct Answer is:
`alpha+beta`
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CHHAYA PUBLICATION-LIMIT-EXERCISE 2 (Very Short Answer Type Questions )
  1. show : underset(xrarr3)"lim"(x^(-6)-3^(-6))/(x^(-4)-3^(-4))=(1)/(6)

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  2. show : underset(hrarr0)"lim"(root(3)(h+1)-1)/(h)=(1)/(3)

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  3. show : underset(xrarra)"lim"(root(3)(x)-root(3)(a))/(x-a)=(1)/(3)a^(-2...

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  4. show : underset(xrarra)"lim"(x^(3/8)-a^(3/8))/(x^(5/3)-a^(5/3))=(9)/(4...

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  5. show : underset(xrarr0)"lim"(1)/(x)[(1+x)^(8)-1]=8

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  6. show : underset(xrarr0)"lim"((1+x)^(9)-1)/((1+x)^(6)-1)=(3)/(2)

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  7. If f(x)=ax^(2)+bx+c , show that , underset(hrarr0)"lim"(f(x+h)-f(x)...

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  8. If f(x)=(1)/(x) , prove that , underset(hrarr0)"lim"(f(2+h)-f(2))/(h)...

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  9. Evaluate the following limits : underset(xrarr0)"lim"(sin2x)/(2x^(2...

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  10. Evaluate the following limits : underset(xrarr(pi)/(2))"lim"(cosx)/...

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  11. Evaluate the following limits : underset(xrarr0)"lim"(sin3x)/(sin2x...

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  12. Evaluate the following limits : underset(xrarrpi)"lim"(sinx)/(pi-x...

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  13. Evaluate the following limits : underset(xrarr(pi)/(2))"lim"(2x-pi...

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  14. Evaluate the following limits : underset(xrarr0)"lim"(sinx^(@))/(x...

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  15. Evaluate : underset(xrarr0)"lim"(e^(4x)-1)/(x)

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  16. Evaluate : underset(xrarr0)"lim"(e^(x)-e^(-x))/(x)

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  17. Evaluate : underset(xrarr0)"lim"(e^(13x)-e^(7x))/(x)

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

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

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  20. Evaluate : underset(hrarr0)"lim"(e^("tan"h)-1)/(h)

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