Home
Class 12
MATHS
Prove that the function f(x) = 5x-3is co...

Prove that the function `f(x) = 5x-3`is continuous at `x = 0`, at `x =-3`and at `x = 5`.

Text Solution

AI Generated Solution

To prove that the function \( f(x) = 5x - 3 \) is continuous at \( x = 0 \), \( x = -3 \), and \( x = 5 \), we will use the definition of continuity. A function is continuous at a point \( c \) if the following three conditions are satisfied: 1. \( f(c) \) is defined. 2. The limit of \( f(x) \) as \( x \) approaches \( c \) exists. 3. The limit of \( f(x) \) as \( x \) approaches \( c \) is equal to \( f(c) \). ### Step 1: Check continuity at \( x = 0 \) ...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    NCERT ENGLISH|Exercise EXERCISE 5.4|10 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    NCERT ENGLISH|Exercise EXERCISE 5.3|15 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    NCERT ENGLISH|Exercise EXERCISE 5.2|10 Videos

  • APPLICATION OF INTEGRALS

    NCERT ENGLISH|Exercise EXERCISE 8.2|7 Videos

  • DETERMINANTS

    NCERT ENGLISH|Exercise All Questions|116 Videos

Similar Questions

Explore conceptually related problems

Show that the function f(x)=2x-|x| is continuous at x=0.

Show that the function f(x)=2x-|x| is continuous at x=0 .

Prove that the function f(x) =2x^2-3x+2 is continuous at at x=1.

Find the values of a and b so that the function f given by f(x) ={1, if x = 5 is continuous at x=3 and x=5 .

Find the values of a and b so that the function f given by f(x)={ax+b , if 3 = 5 is continuous at x=3 and x=5.

Prove that the function defined by f(x) = t a n x is a continuous function.

Examine whether the function f given by f(x)=x^(3) is continuous at x =0

If the function f(x)=(sin10 x)/x , x!=0 is continuous at x=0 , find f(0) .

Prove that f(x)=sqrt(|x|-x) is continuous for all xgeq0 .

Prove that f(x)=sqrt(|x|-x) is continuous for all xgeq0.

Home
Profile