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Find the limit lim(x->4) [(cosa) x -(sina) x -cos2a)/(x-4)] 0

Find the limit
lim(x->4) [(cosa)x-(sina)x-cos2a)/(x-4)]
0
 

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
Hello Student,
Please find answer to your question below

L = \lim_{x\rightarrow 4}\frac{(cosa)^{x}-(sina)^{x}-cos2a}{x-4}
L = \lim_{x\rightarrow 4}\frac{((cosa)^{x}-(sina)^{x})-(cos^{2}a-sin^{2}a)}{x-4}
L = \lim_{x\rightarrow 4}\frac{((cosa)^{x}-(sina)^{x})-(cos^{2}a-sin^{2}a)(cos^{2}a+sin^{2}a)}{x-4}
L = \lim_{x\rightarrow 4}\frac{((cosa)^{x}-(sina)^{x})-(cos^{4}a-sin^{4}a)}{x-4}
L = \lim_{x\rightarrow 4}\frac{(cos^{4}a)((cosa)^{x-4}-1)-sin^{4}a((sina)^{x-4}-1))}{x-4}
L = \lim_{x\rightarrow 4}\frac{(cos^{4}a)((cosa)^{x-4}-1)}{x-4}-\lim_{x\rightarrow 4}\frac{sin^{4}a((sina)^{x-4}-1)}{x-4}
L = (cos^{4}a).ln(cosa)-sin^{4}a.ln(sina)

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