Home
Class 12
MATHS
Let f(x)={{:(5x-4",",0ltxle1),(4x^(3)-3x...

Let `f(x)={{:(5x-4",",0ltxle1),(4x^(3)-3x",",1ltxlt2.):}`
Find `lim_(xto1)f(x).`

Text Solution

Verified by Experts

The correct Answer is:
Thus `RHL=LHL=1` So `lim_(xto1)f(x)` exists and is equal to 1.
Promotional Banner

Similar Questions

Explore conceptually related problems

If f(x) = {(x-5,x le1),(4x^(2)-9, 1ltxlt2),(3x+4, x ge2):} then f^(')(2^(+)) =

Show that the function f defined as follows, is continuoius at x=2, but not differentiable at x=2. f(x)={{:(3x-2, 0 lt x le 1),(2x^(2)-x, 1 lt x le 2),(5x-4,x gt 2):} .

Given f(x) ={{:( ( x)/( |x|)),(2),( xne 0),( x= 0) :} } "find " lim _( xto 0) f(x)

Find lim_(xrarr1)f(x) , where f(x)={{:(x^(2)-1",",xle1),(-x^(2)-1",",xgt1):}

Let f : R rarrR be defined by f(x)={{:(2x ,,,x gt3 ),(x^2,,,1 lt xle3),(3x,,,x le1):} Then f(-1) + f(2) + f(4) is

Let f: RrarrR be defined by f(x)={(2x , xgt3),(x^(2), 1ltxle3),(2x,xle1):} Then f(-1)+f(2)+f(4) is

Let f(x) = {{:(x^(2) - 1, 0 lt x lt 2),(2x + 3, 2 le x lt 3):} , the quadratic equation whose roots are lim_(x rarr 2^(-)) f(x) and lim_(x rarr 2^(+)) f(x) is :

If f(x)=xtan^(-1)x , then lim_(xto1)(f(x)-f(1))/(x-1)=

If f(x)=3x^(2)+12x-1,-1lexle2,=37-x,2ltxle3 , then :

Prove that f(x) = ={:( ax^(2) -3x+ 4 " when "xlt 1 ),( 3" when "x=1 ),( bx+ 5" when " xgt 1) :}and "if" Lim _( xto 1) f(x) =f(1) "then find the values of a and b."