Determine whether the following limits exist, and where they exist, determine th

Question

Determine whether the following limits exist, and where they exist, determine their limiting value. Show your working and explain your method. In this question the values of your parameters are: a = 1, b = 2, c = 3, d = 4, k = 5, m = 6, n = 7 lim x rightarrow 0 cos (cx) - cos (dx)/sin2 (kx) NB the exponents in Q3(a) is 2;two, a square. The limit is at zero.

Explanation / Answer

lim x-->0 cos 3x - cos 4x / sin^2 5x applyin L hosp rule we get, -3 sin 3x + 4 sin 4x / 5 sin 10x = -3/5 sin 3x/sin 10x + 4/5 sin 4x/sin 10 x = -3/5 * 3/10 sin 3x/3x/sin 10x/10x + 4/5 * 4/10 sin 4x/4x/sin 10 x/10x = 16/50 - 9/50 = 7/50

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