Home
Class 11
MATHS
Evaluate lim(xrarr0)((3^(x)-2^(3x))/(x))...

Evaluate `lim_(xrarr0)((3^(x)-2^(3x))/(x)).`

Text Solution

Verified by Experts

`lim_(xto0)((3^(x)-2^(3x))/(x))=lim_(xto0){((3^(2x)-1)-(2^(3x)-1))/(x)}`
`=lim_(xto0)((3^(2x)-1)/(x))-lim_(xto0)((2^(3x)-1)/(x))`
`=lim_(xto0){((3^(2x)-1)/(2x)).2}-lim_(xto0){((2^(3x)-1)/(3x)).3}`
`=2. lim_(2xto0)((3^(2x)-1)/(2x))-3.lim_(3xto0)((2^(3x)-1)/(3x))`
`=(2log3-3log2)" "[becauselim_(yto0)((a^(y)-1)/(y))=loga]`
`=[log(3)^(2)-log(2)^(3)]=(log9-log8)=log((9)/(8)).`
Promotional Banner

Topper's Solved these Questions

  • LIMIT

    RS AGGARWAL|Exercise EXERCISE 27A|40 Videos

  • LIMIT

    RS AGGARWAL|Exercise EXERCISE 27B|72 Videos

  • LIMIT

    RS AGGARWAL|Exercise EXERCISE 27C|15 Videos

  • HYPERBOLA

    RS AGGARWAL|Exercise EXERCISE 24|23 Videos

  • LINEAR INEQUATIONS (IN ONE VARIABLE)

    RS AGGARWAL|Exercise EXERCISE 6B|12 Videos

Similar Questions

Explore conceptually related problems

Evalvate lim_(xrarr0)((3^(x)-2^(x))/(x)).

Evaluate lim_(xrarr0)((3^(2x)-1)/(2^(3x)-1)).

Evalute lim_(xrarr0)((e^(3x)-1)/(x)).

Evaluate lim_(xrarr0)((x^(3)cotx)/(1-cosx)).

Evaluate lim_(xrarr0) (1+x)^(1/x)

Evaluate lim_(xrarr0)((1+x)^(n)-1)/(x)

Evaluate: (i)lim_(xrarr0)((e^(-x)-1)/(x))(ii)lim_(xrarr0)((e^(x)-e^(-x))/(x))(iii)lim_(xrarr0)((e^(x)+e^(-x)-2)/(x^(2)))

lim_(xrarr0) (x^(2)-3x+2)

Evaluate: lim_(xrarr0) ((3+x)^(1//2)-(3-x)^(1//2))/(x)

Evaluate the following limits: lim_(xrarr0)((a^(x)-b^(x))/(x))