Question

मान लीजिए $f(x) = \lim_{x\rightarrow 0}f(x), \,where \,f(x) = \right \begin{cases} a + bx , \,\,\,\,\,x \ \textless \ 1 \\\atop {4}, \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, x = 1 \\\atop {b - ax}, \, \,\,\,\,\,\,\,\,\,\,\,\, x \ \textgreater \ 1 \end{cases}$ और यदि $\lim_{x\rightarrow1}f(x) = f(1)$ तो a और b के संभव मान क्या है?

Answer 1

x/rigtharrow of textless atop begin

Answer 2

a और b के संभव मान a = 0  b = 4

Step-by-step explanation:

Lim x → 1   f(x)

f(x) =  a + bx  x < 1

          4        x = 1

      b - ax     x > 1

Lim x → 1   f(x)   = f(1)

LHL = RHL = f(1)

LHL = x = 1- h  h → 0  f(x) = a + bx

RHL x = 1+ h h → 0  f(x) = b - ax

LHL

= Lim h → 0    a + b(1 - h)

= a + b(1 - 0)

= a + b

RHL

= Lim h → 0    b - a(1 + h)

= b - a (1 + 0)

= b - a

LHL = RHL = f(1)

a + b = b - a = 4

=> a + b = 4

    -a  + b = 4

=> 2b = 8

=> b = 4

 a = 0

a और b के संभव मान a = 0  b = 4

और पढ़ें

सीमाओं के मान प्राप्त कीजिए :  [tex]\lim_{x\rightarrow3}\dfrac{x^4 - 81

brainly.in/question/15778085

सीमाओं के मान प्राप्त कीजिए

brainly.in/question/15778083