Home
Class 11
MATHS
Evalute lim(xrarr0)((e^(3x)-1)/(x))....

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

Text Solution

Verified by Experts

`lim_(xto1)((e^(3x)-1)/(x))=lim_(3xto0){((e^(3x)-1)/(3x))xx3}" "[because(xto0)implies(3xto0)]`
`=3xxlim_(yto0)((e^(y)-1)/(y))where y=3x`
`=(3xx1)=3" "[becauselim_(xto0)((e^(y)-1)/(y))=1].`
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

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)))

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

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

Evalvate lim_(xrarr0)((1+x)^(4)-1)/(x).

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

lim_(xrarr0) ((x+1)^(5)-1)/(x)

Evaluate : lim_(xrarr0 )(e ^(sinx)-1)/(x)

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

Evaluate the following limits: lim_(xrarr0)((e^(x)-x-1)/(x))

Evaluate the following limits: lim_(xrarr0)((e^(4x)-1)/(x))