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lim(h rarr 0)1/h(1/(sqrt(x+h))-1/(sqrt(x...

`lim_(h rarr 0)1/h(1/(sqrt(x+h))-1/(sqrt(x)))`

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Verified by Experts

The correct Answer is:
`(-1)/(2x^(3//2))`
Given limit `=lim_(hto0){((sqrtx-sqrt(x+h)))/(h(sqrt(x+h))sqrtx)xx((sqrtx+sqrt(x+h)))/((sqrtx+sqrt(x+h)))}`
`=lim_(hto0)(-h)/(h(sqrt(x+h))sqrtx(sqrtx+sqrt(x+h)))`
`=lim_(hto0)(-1)/((sqrt(x+h))sqrtx(sqrt(x+h)))=(-1)/(2x^(3//2)).`
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RS AGGARWAL-LIMIT-EXERCISE 27A
  1. Evaluate the following limits: lim(xrarra)((sqrtx-sqrta)/(x-a)).

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  2. Evaluate the following limits: lim(hto0)((sqrt(1+h)-1)/(h))

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  3. lim(h rarr 0)1/h(1/(sqrt(x+h))-1/(sqrt(x)))

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  4. Evaluate the following limits: lim(xrarr0)((sqrt(x+h)-sqrtx)/(x))

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  5. Evaluate the following limits: lim(xrarr0)((sqrt(2-x)-sqrt(2+x))/(x))

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  6. Evaluate the following limits: lim(xrarr0)((sqrt(1+x+x^(2))-1)/(x))

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  7. Evaluate the following limits: lim (x->1)((sqrt(2-x)-1)/(1-x))

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  8. Evaluate the following limits: lim(xrarr0)((2x)/(sqrt(x+2)-sqrt(2-x))...

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  9. Evaluate the following limit: (lim)(x->1)(sqrt(3+x)-sqrt(5-x))/(x^2-1)

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  10. Evaluate the following limits: lim(xrarr2)((x^(2)-4)/(sqrt(x+2)-sqrt...

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  11. Evaluate the following limits: lim(xrarr4)((3-sqrt(5+x))/(1-sqrt(5-x)...

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  12. Evaluate the following limits: lim(xrarr1)((sqrt(a+x)-sqrta)/(xsqrt(...

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  13. Evaluate the following limits: lim(xrarr0)((sqrt(1+x^(2))-sqrt(1+x))...

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  14. lim(x->1) ((x^4-3x^2+2)/(x^3-5x^2+3x+1))

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  15. Evaluate the following limits: lim(xrarr2)((3^(x)+3^(3-x)-12)/(3^(3-...

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  16. Evaluate the following limits: lim(xrarr0)((e^(4x)-1)/(x))

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  17. Evaluate the following limits: lim(xrarr0)((e^(2+x)-e^(2))/(x))

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  18. Evaluate the following limits: lim(xrarr4)((e^(x)-e^(4))/(x-4))

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  19. Evaluate the following limits: lim(xrarr0)((e^(2+x)-e^(2))/(x))

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  20. Evaluate the following limits: lim(xrarr0)((e^(x)-x-1)/(x))

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