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Can any one plz sovle this to me?
Find the value of constant k so that
f (x) = { sin 3x / x x =0
k x=0
Will be continuous at x=0.
Thanks for ur help in advance
4 Answers
- 1 decade agoFavorite Answer
ok I got what do u want
.......{ (sin3x)/x --------->when x=/= 0
f(x)={ k ----------------------> when x=0
so u must get
limit (sin3x)/x = 3
x--->0
so k must be 3
- MadhukarLv 71 decade ago
I assume you mean
f(x) = (sin 3x) / x, for x ≠ 0
f(x) = k, for x = 0.
For f to be continuous at 0, f(0) = lim (x-> 0) f(x)
=> k = lim (x -> 0) (sin 3x) / x
=> k = lim (x -> 0) [(sin 3x) / 3x] * 3
=> k = 3
(because x -> 0 => 3x -> 0 and lim (3x -> 0) (sin 3x) / 3x = 1)
