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Prove that, lim(x rarr 0) (5^(x)-4^(x))/...

Prove that, `lim_(x rarr 0) (5^(x)-4^(x))/(x)=log_(e)((5)/(4))`

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CHHAYA PUBLICATION-LIMIT-EXAMPLE
  1. Evaluate: lim(x rarr 1) (e^(logx)-1)/(e^(x-1)-1)

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  2. Evaluate: lim(x rarr 2) (e^(x)-e^(2))/(x-2)

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  3. Prove that, lim(x rarr 0) (5^(x)-4^(x))/(x)=log(e)((5)/(4))

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  4. Evaluate: lim(x rarr 0) log(1+alphax)/(e^(2x)-1)

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  5. Evaluate: lim(x to 0)(e^(ax)-1)/(sinbx)

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  6. Evaluate: lim(x to 0)(sinx)/(log(e)(1+x)^(1/4)

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  7. Evaluate: lim(x to 0)((e^(x)-1)log(1+x))/(sin^(2)x)

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  8. Evaluate: lim(x to 0)(3^(x)-1)/((4+x)^(1/2)-2)

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  9. Show that , lim(x rarr 0)(3^(x)+3^(-x)-2)/(x^(2)

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  10. Show that, lim(x rarr 0) log(1+x^(3))/(sin^(3)x)= 1

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  11. If lim(x to 0)(1+x)^(1/x)=e, prove that lim(x to 0)(1+3x)^(((x+2))/(x)...

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  12. Evaluate the following limits: lim(x to 3)sin(e^(x-3)-1)/(log(x-2))

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  13. Evaluate the following limits: lim(x to 0)[(1)/(x)-log(1+x)/(x^(2))]

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  14. Evaluate the following limits: lim(x rarr 0)(xe^(x)-log(1+x))/(x^(2))

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  15. Find the value of : lim(x rarr oo) ((x+5)/(x+1))^(5)

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  16. Find the value of : lim(x rarr oo) ((x+5)/(x-1))^(5)

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

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  18. Does underset(xrarr2)"lim"(x^(2)-4)/(x-2) exist If so , find its val...

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

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  20. Draw the graph of y=f(x)=(x^(2))/(x) and from the graph examine wheth...

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