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