limitof(sin3x)/(5x^3-4x)asxapproaches0
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limitof(sin3x)/(5x^3-4x)asxapproaches0
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We can use the fact that sin(x) is approximately equal to x when x is very small, and use L'H?pital's rule to evaluate the limit:
lim x → 0 sin(3x)/(5x^3 - 4x)
= lim x → 0 (3x)/(5x^3 - 4x) (using sin(3x) ≈ 3x when x is small)
= lim x → 0 3/(15x^2 - 4)
= 3/(-4) (using L'H?pital's rule)
= -3/4
Therefore, the limit of sin(3x)/(5x^3 - 4x) as x approaches 0 is -3/4.
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