निम्न प्रकार से परिभाषित फलन की सातत्यता की जाँच x = 0 पर कीजिएf(x) = \left \{ {{x^{2} sin1/x } यदि x \neq 0 \atop {0} यदि x = 0} \right
Answers
f(x) संतत है x ∈ R
Step-by-step explanation:
f(x) = x²Sin(1/x) यदि x ≠ 0
0 यदि x = 0
x < 0 , x = 0 , x > 0
x < 0
f(x) = x²Sin(1/x)
संतत है यदि
Lim (x → c) f(x) = f(c) c < 0
Lim (x → c) f(x) = c²Sin(1/c) c≠ 0
f(c) = c²Sin(1/c)
LHS = RHS
f(x) , x < 0 पर संतत है
x > 0
f(x) = x²Sin(1/x)
संतत है यदि
Lim (x → c) f(x) = f(c) c > 0
Lim (x → c) f(x) = c²Sin(1/c) c≠ 0
f(c) = c²Sin(1/c)
LHS = RHS
f(x) , x > 0 पर संतत है
x =0 , संतत है यदि
LHL = RHL = f(0)
LHL = Lim (h → 0) f(0 - h) = (-h)²Sin(1/(-h)) = - h²Sin(1/h) = 0
RHL = Lim (h → 0) f(0 + h) = (h)²Sin(1/(h)) = h²Sin(1/h) = 0
f(0) = 0
LHL = RHL = f(0)
f(x) , x = 0 पर संतत है
f(x) संतत है x ∈ R
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