Math, asked by babusambit5370, 9 months ago

\begin{cases}2x यदि x < 0 \\ 0 यदि 0 \le x \le 1 \\ 4x यदि x > 1\end{cases}

Answers

Answered by amitnrw
0

फलन f(x)  x ∈ R  x≠ 1  पर संतत है

Step-by-step explanation:

f(x) = 2x   यदि  x < 0

        0   यदि  0 ≤ x ≤ 1

        4x  यदि   x > 1

x < 0 , x = 0    0 < x  < 1 , x  = 1  ,   x >  1

x < 0

f(x) = 2x

Lim (x → c)  = 2x    c < 0

f(c) = 2c

Lim (x → c) = f(c)

फलन f(x) ,  x < 0 पर संतत है

0 < x < 1

f(x) = 0

Lim (x → c)  = 0    0 < c < 1

f(c) = 0

Lim (x → c) = f(c)

फलन f(x) ,   0 < x < 1 पर संतत है

x > 1

f(x) = 4x

Lim (x → c)  = 4c    c > 1

f(c) = 4c

Lim (x → c) = f(c)

फलन f(x) ,  x > 1  पर संतत है

x = 0

संतत है यदि

LHL = RHL = f(0)

LHL = Lim (h → 0)  f(0 - h)  = 2(-h)  = 0

RHL =  Lim (h → 0)  f(0 + h)  = 0

f(0) = 0

LHL = RHL = f(0)

फलन f(x) ,  x = 0 पर संतत  है

x = 1

संतत है यदि

LHL = RHL = f(1)

LHL = Lim (h → 0)  f(1 - h)  = 0

RHL =  Lim (h → 0)  f(1 + h)  = 4(1 + h) = 4

0 ≠  4

LHL ≠ RHL

फलन f(x) ,  x =1 पर संतत  नहीं  है

फलन f(x)  x ∈ R  x≠ 1  पर संतत है

और  जानें:

फलन f(x) = 5x – 3, x = 0, x = – 3 तथा x = 5 पर संतत है

brainly.in/question/15285693

X = 3 पर फलन f(x) = 2x^{2} – 1 के सातत्य की जाँच कीजिए।

brainly.in/question/15285688

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