Question

$\lim_{x\rightarrow0}f(x) \,and \,\lim_{x\rightarrow1}f(x), \,ज्ञात कीजिए , जहाँ \,f(x) = \right \begin{cases}{2x + 3}, \,\,\,\,\,x \leq 0\atop 3(x + 1), \, x \ \textgreater \ 0 \end{cases}$

Answer 1

Lim x → 0   f(x)  = 3 , Lim x → 1   f(x)  = 6

Step-by-step explanation:

Lim x → 0   f(x)  Lim x → 1   f(x)

f(x) =  2x + 3   x ≤ 0

        3(x + 1)   x > 0

LHL = x = 0- h  h → 0  f(x) =  2x + 3

RHL x = 0+ h  f(x) = 3(x + 1)

Lim h → 0    2(0 - h)  + 3

= 2(0- 0) + 3

= 0 + 3

= 3

RHL Lim h → 0    3(0 + h + 1)

= 3(0 +0 +  1)

= 3 (1)

= 3

LHL = RHL

f(0) = 2x + 3 = 2(0) + 3 = 3

Lim x → 0   f(x)  = 3

Lim x → 1   f(x)

x > 0  f(x) = 3(x + 1)

f(1) = 3(1 + 1) = 6

Lim x → 1   f(x)  = 6

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