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Prove that underset(hrarr-2)"lim"(h^(5...

Prove that
`underset(hrarr-2)"lim"(h^(5)+32)/(h+2)=80`

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underset(hrarr0)"lim"(3h^(2)-2h)/(h)= ?

underset(xrarr2)"lim"(x^(5)-32)/(x-2)= ?

Prove that underset(xrarroo)"lim"(1)/(x)=0 .

If f(x)=(1)/(x) , prove that , underset(hrarr0)"lim"(f(2+h)-f(2))/(h)=-(1)/(4)

underset(hrarr1)"lim"(2h^(2)-2h+9)^(3/2)= ?

Evaluate : underset(hrarr0)"lim"(e^(5h)-1)/(3h)

Prove that underset(hrarr0)"lim"(root3(x+h)-root3(x))/(h)=(1)/(3)x^(-2/3)

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

Prove that underset(xrarra)"lim"((x+5)^(5//2)-(a+5)^(5//2))/(x-a)=(5)/(2)(a+5)^(3//2)

Prove that underset(xrarry)"lim"(x^(9//2)-y^(9//2))/(x^(5//2)-y^(5//2))=(9)/(5)y^(2)

CHHAYA PUBLICATION-LIMIT-IIIustrative Examples
  1. Evaluate : underset(xrarr0)"lim"(sqrt(1-x^(3))-sqrt(1-x))/(sqrt(1+x^...

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  2. Evaluate : underset(xrarr3)"lim"(sqrt(x-3)+sqrt(x)-sqrt(3))/(sqrt(x...

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  3. Prove that underset(hrarr-2)"lim"(h^(5)+32)/(h+2)=80

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  4. Prove that underset(xrarr0)"lim"((1+x)^(1//2)-1)/((1+x)^(1//3)-1)=(3...

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  5. Prove that underset(xrarry)"lim"(x^(9//2)-y^(9//2))/(x^(5//2)-y^(5//...

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  6. Prove that underset(hrarr0)"lim"(root3(x+h)-root3(x))/(h)=(1)/(3)x^(...

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  7. Prove that underset(xrarra)"lim"((x+5)^(5//2)-(a+5)^(5//2))/(x-a)=(...

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  8. Evaluate : underset(xrarr0)"lim"(root(3)(1+x)-root(3)(1-x))/(x)

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  9. Evaluate : underset(xrarr2)"lim"(2-sqrt(2+x))/(root(3)(2)-root(3)(4-x)...

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  10. Evaluate :underset(xrarr0)"lim"(tanx^(@))/(x)

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

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  12. underset(xrarr(pi)/(2))"lim"(cosx)/((pi)/(2)-x) =

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  13. Evaluate :underset(xrarrpi)"lim"(sin3x)/(sin2x)

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  14. Evaluate :underset(xrarrpi)"lim"(1+cosx)/(x-pi)^(2)

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  15. Evaluate :underset(xrarr0)"lim"(sinx(1-cosx))/(x^(3))

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  16. Evaluate :underset(xrarr0)"lim"(x^(2)-tan2x)/(tanx)

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  17. Evaluate :underset(xrarr0)"lim"(cosec"x-cotx)/(x)

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  18. Evaluate :underset(xrarr0)"lim"(cos5x-cos7x)/(cosx-cos5x)

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  19. Evaluate :underset(xrarry)"lim"(sin^(2)x-sin^(2)y)/(x^(2)-y^(2))

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  20. Evaluate : underset(xrarr(pi)/(2))"lim"((pi)/(2)-x)tanx

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