Evaluate
Lim x tends to pi sin3x-3sinx/ (pi-x )^3
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8
your answer for above question
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Najminsultana:
But ans is -4
Answered by
23
Lim(x→π) {sin3x - 3sinx}/(π - x)³
Let x = h + π
then,
Lim(h-->0) { sin3(h + π) - 3sin(h + π)}/{π - π-h)³}
Lim(h-->0) { sin(3h + 3π) +3sinh}/(-h)³
Lim(h--->0) {-sin3h + 3sinh }/-h³
Lim(h--->0) { 3sinh - sin3h }/h³
we know, sin3A = 3sinA - 4sin³A
so, 4sin³A = 3sinA - sin3A use this application here,
Lim(h--->0) {4sin³h}/h³
Lim(h--->0)4 {sinh/h}³
but we know, from rule Lim(r-->0) sinr/r = 1
so, Lim(h--->0) 4{sinh/h}³ = 4 × 1³ = 4
hence, answer is 4
Let x = h + π
then,
Lim(h-->0) { sin3(h + π) - 3sin(h + π)}/{π - π-h)³}
Lim(h-->0) { sin(3h + 3π) +3sinh}/(-h)³
Lim(h--->0) {-sin3h + 3sinh }/-h³
Lim(h--->0) { 3sinh - sin3h }/h³
we know, sin3A = 3sinA - 4sin³A
so, 4sin³A = 3sinA - sin3A use this application here,
Lim(h--->0) {4sin³h}/h³
Lim(h--->0)4 {sinh/h}³
but we know, from rule Lim(r-->0) sinr/r = 1
so, Lim(h--->0) 4{sinh/h}³ = 4 × 1³ = 4
hence, answer is 4
see clearly my answer
-h^3=-h
(-h)³ = -h³
then i use '-' for above (-sin3h + 3sinh)/-h³
(3sinh - sin3h)/h³
Then -4×lim h tend to 0 (sinh/h )^3
why you didn't get it ? . why you take -4
here it is clear that
4 is answer . see my answer sincerely . we use formula, sin3A = 3sinA - 4sin³A then, 4sin³A = 3sinA - sin3A
then, lim(h-->0) 4sin³h/h³ = 4
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