Home
Class 12
MATHS
Redfine the following functions at the p...

Redfine the following functions at the point x=0 so as to make them continuous:
`(a) f(x)=(tan x)/(x)` (b) `f(x)=(5x^2-3x)/(2x)`
(f ) `f(x)=(sqrt(1+x)-1)/(x)` (d) `f(x)=(sin^2x)/(1-cosx)`

Text Solution

Verified by Experts

The correct Answer is:
`(a) f(0)=1; (b) f(0)=-3/2; (c) f(0)=1/2; (d) f(0)=2`
Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION OF MATHEMATICAL ANALYSIS

    IA MARON|Exercise Arithmetical Operations on Continous Function, Continuity of a Composite Functions|2 Videos

  • INTRODUCTION OF MATHEMATICAL ANALYSIS

    IA MARON|Exercise The Properties of a Function. Continuous a Closed Interval. Continuity of an Inverse Function.|2 Videos

  • INTRODUCTION OF MATHEMATICAL ANALYSIS

    IA MARON|Exercise One-Sided Limits|3 Videos

  • INDEFINITE INTEGRALS, BASIC METHODS OF INTEGRATION

    IA MARON|Exercise 4.4. Reduction Formulas|2 Videos

  • THE DEFINITE INTEGRAL

    IA MARON|Exercise 6 . 8 (Additional Problems)|3 Videos

Similar Questions

Explore conceptually related problems

Examine the following functions for continuity. (a) f(x)=x-5 (b) f(x)=1/(x-5) (c) f(x)=(x^2-25)/(x+5) (d) f(x)=|x-5|

For which of the following functions f(0) exists such that f(x) is continuous at x=0f(x)=(1)/((log_(e)|x|) b.f(x)=(cos((sin|x|)/(x))) c.f(x)=x sin((pi)/(x)) d.f(x)=(1)/(1+2^( cot x))

Find the one-sided limits of the following functions as x to 0 (a) f(x)=(1)/(2-2^(1//x)) (b) f(x)=e^(1//x) . (c ) f(x)=(|sin x|)/(x)

Which of the following function from Z to itself are bijections? f(x)=x^(3)( b) f(x)=x+2f(x)=2x+1( d )f(x)=x^(2)+x

Which of the following is an even function a )f(x)=(a^(x)+a^(-x))/(a^(x)-a^(-x)) b) f(x)=(a^(x)+1)/(a^(x)-1) c) f(x)=x(a^(x)-1)/(a^(x)+1)(d)f(x)=log_(2)(x+sqrt(x^(2)+1))

In which of the following functions is Rolles theorem applicable? (a)f(x)={x ,0lt=x<1 0,x=1on[0,1] (b)f(x)={(sinx)/x ,-pilt=x<0 0,x=0on[-pi,0) (c)f(x)=(x^2-x-6)/(x-1)on[-2,3] (d)f(x)={(x^3-2x^2-5x+6)/(x-1)ifx!=1,-6ifx=1on[-2,3]