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rainbow22
 3 years ago
lim x>0 [(3sin4x)/(sin 3x)] = 4 lim x>0 [(sin 4x/4x)x(3x/sin3x)]
How is this true?
rainbow22
 3 years ago
lim x>0 [(3sin4x)/(sin 3x)] = 4 lim x>0 [(sin 4x/4x)x(3x/sin3x)] How is this true?

This Question is Closed

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2to get 4x in the denominator, 4x is multiplied in numerator and denominator. got some idea?

Algebraic!
 3 years ago
Best ResponseYou've already chosen the best response.1Multiply the whole thing by (12x/12x). rearrange.

dumbcow
 3 years ago
Best ResponseYou've already chosen the best response.0you can also use L'Hopitals Rule Take derivative of both top and bottom, then reevaluate the limit

rainbow22
 3 years ago
Best ResponseYou've already chosen the best response.0But it would be undefined if I took the limit of the bottom

Algebraic!
 3 years ago
Best ResponseYou've already chosen the best response.1Always with l'Hopital's. You'd think it was the only thing anyone ever retained from calc. class.

rainbow22
 3 years ago
Best ResponseYou've already chosen the best response.0I haven't learned it yet :(

Algebraic!
 3 years ago
Best ResponseYou've already chosen the best response.1They're learning about sinc(x) here anyway ... that's a few lectures before the class on l'Hopital's.

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2dw:1347162711646:dw got it now?

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2just use sin t / t when limit t>0 = 1 formula.

Algebraic!
 3 years ago
Best ResponseYou've already chosen the best response.1@hartnn what did you multiply by? It's cut off in the sketch.

rainbow22
 3 years ago
Best ResponseYou've already chosen the best response.0Why is it that .... the 4 is moved outside the limit?

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2multiplied by 4x in num and denom, and it can be seen,iguess

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2the 4 is constant and constants can be moved outside the limit

rainbow22
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1347163083569:dw

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2now 12x / sin 3x can again be written as 4 * (3x/sin 3x) and using same limit again its 4*1= 4 ok?

Algebraic!
 3 years ago
Best ResponseYou've already chosen the best response.1dw:1347163221313:dw

rainbow22
 3 years ago
Best ResponseYou've already chosen the best response.0Oh, I get it now! Thank you guys SO MUCH!
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