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lim X>0 (1-cos4X+Xsin3X/X*X)

 Aug 7, 2015

Best Answer 

 #2
avatar+30397 
+5

cos(4x) → 1 - 8x2 + 32x4/3 + ...

sin(3x) → 3x - 9x3/2 + ...

 

so: (1- cos(4x) + x*sin(3x))/x2 → (1 - (1 -  8x2 + 32x4/3 + ...) +x*(3x - 9x3/2 + ...))/x2

 → (8x2 + 3x2 + higher order terms in x)/x2 →  11 + higher order terms in x

 

Hence in the limit as x → 0,  (1- cos(4x) + x*sin(3x))/x2 → 11

.

 Aug 7, 2015
 #1
avatar+109806 
+5

Your question does not make sense.  Perhaps you mean something like this?

 

$$\\\displaystyle\lim_{ X\rightarrow 0} \frac{1-cos4X+Xsin3X}{X*X}\\\\$$

.
 Aug 7, 2015
 #2
avatar+30397 
+5
Best Answer

cos(4x) → 1 - 8x2 + 32x4/3 + ...

sin(3x) → 3x - 9x3/2 + ...

 

so: (1- cos(4x) + x*sin(3x))/x2 → (1 - (1 -  8x2 + 32x4/3 + ...) +x*(3x - 9x3/2 + ...))/x2

 → (8x2 + 3x2 + higher order terms in x)/x2 →  11 + higher order terms in x

 

Hence in the limit as x → 0,  (1- cos(4x) + x*sin(3x))/x2 → 11

.

Alan Aug 7, 2015

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