Grade 12Differential Calculus

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

Lovey

12 Years agoGrade 12

1 Answer

Jitender Singh

Approved Tutor Answer12 Years ago

Ans:
Hello Student,
Please find answer to your question below

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