Home
Class 11
MATHS
Evaluate the following limit: lim(x->0)(...

Evaluate the following limit: `lim_(x->0)(5^x+3^x+2^x-3)/x`

Text Solution

Verified by Experts

`lim_(x->0)(5^x+3^x+2^x-3)/x`
`=lim_(x->0)(5^x-1+3^x-1+2^x-1)/x`
`=lim_(x->0)(5^x-1)/x+lim_(x->0)(3^x-1)/x+lim_(x->0)(2^x-1)/x`
`=log5+log3+log2`
`=log(5xx3xx2)`
`=log 30`
Promotional Banner

Topper's Solved these Questions

  • INTRODUCTIONS TO 3-D COORDINATE GEOMETRY

    RD SHARMA|Exercise Solved Examples And Exercises|114 Videos

  • LINEAR INEQUATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|163 Videos

Similar Questions

Explore conceptually related problems

Evaluate the following limit: (lim)_(x->0)(t a n2x-x)/(3x-sin x)

Evaluate the following limit : (lim)_(x->0)((a^x+b^x+c^x)/3),\ (a , b ,\ c >0)

Evaluate the following limit: (lim)_(x->0)(1-cos5x)/(3x^2)

Evaluate the following limits: lim_(xrarr0)(x cot2x)

Evaluate the following limit: (lim)_(x->0)(e ^(x^2)-3^(3x))/(sin((x^2)/2)-sinx)

Evaluate of the following limit: (lim)_(x->0)(e^x-e^(-x)-2x)/(x^3)

Evaluate the following limit: (lim)_(x rarr2)(3-x)

Evaluate the following limits: lim_(xrarr0)((3^(2+x)-9)/(x))

Evaluate the following limits: lim_(xrarr0)((2^(x)-1)/(x))

Evaluate the following limits: lim_(xrarr3)((x^(2)-4x+3)/(x^(2)-2x-3))