Home
Class 12
MATHS
Let f(x)={{:(x+1", "xgt0),(2-x", "xle0):...

Let `f(x)={{:(x+1", "xgt0),(2-x", "xle0):}"and"g(x)={{:(x+3", "xlt1),(x^(2)-2x-2", "1lexlt2),(x-5", "xge2):}`
Find the LHL and RHL of g(f(x)) at x=0 and, hence, find `lim_(xto0) g(f(x)).`

Text Solution

Verified by Experts

`xrarr0^(-)impliesf(x)rarrf(0^(-))=2^(+)" "("using" f(x)=2-x)`
or `" "underset(xto0^(-))limg(f(x))=g(2^(+)-3" "("using" g(x)=x-5`)
Also, `xto0^(+)impliesf(x)torarrf(0^(+))=1^(+)" "("using" f(x)=x+1)`
or `" "underset(xto0^(+))limg(f(x))=g(1^(+))=-3" "("using" g(x)=x^(2)-2x-2)`
Hence, `underset(xto0)limg(f(x))` exists and is equal to -3. Therefore,
`underset(xto0)limg(f(x))=-3`
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE PUBLICATION|Exercise Solved Examples|15 Videos

  • LIMITS

    CENGAGE PUBLICATION|Exercise EXERCISE 2.1|10 Videos

  • JEE 2019

    CENGAGE PUBLICATION|Exercise Chapter 10|8 Videos

  • LINEAR COMBINATION OF VECTORS, DEPENDENT AND INDEPENDENT VECTORS

    CENGAGE PUBLICATION|Exercise DPP 1.2|10 Videos

Similar Questions

Explore conceptually related problems

Let f(x)={x+1,x >0, 2-x ,xlt=0 and g(x)={x+3,x 0)g(f(x)).

If |f(x)|lex^(2), then prove that lim_(xto0) (f(x))/(x)=0.

let f(x)={( int_0^x|1-t|dt, xgt1),(x-1/2, xle1):} then

Let f(x)={(2x+a",",x ge -1),(bx^(2)+3",",x lt -1):} and g(x)={(x+4",",0 le x le 4),(-3x-2",",-2 lt x lt 0):} If a=2 and b=3, then the range of g(f(x)) is

Let f(x)={(2x+a",",x ge -1),(bx^(2)+3",",x lt -1):} and g(x)={(x+4",",0 le x le 4),(-3x-2",",-2 lt x lt 0):} If the domain of g(f(x))" is " [-1, 4], then

Let f(x)={{:(1+(2x)/(a)", "0lexlt1),(ax", "1lexlt2):}."If" lim_(xto1) "f(x) exists, then a is "

Letf(x)={{:(x+1,", "if xge0),(x-1,", "if xlt0):}".Then prove that" lim_(xto0) f(x) does not exist.

Evaluate lim_(xto0) (e^(x)-1-x)/(x^(2)).

If f(x)={(x[x], 0lexlt2),((x-1)[x],2lexle3):} , then f(x) is

If f(x)={{:(x","" "xlt0),(1","" "x=0),(x^(2)","" "xgt0):}," then find " lim_(xto0) f(x)" if exists.