Question

If the given fun is continuous at x 0 find k 1-cos4x/6x^2 if x not =0 3k if x=0

Answer 1

Answer :

for f(x) to be continuous at x=0

for f(x) to be continuous at x=0lim _ f (x)=f (0)

for f(x) to be continuous at x=0lim _ f (x)=f (0)x->0

for f(x) to be continuous at x=0lim _ f (x)=f (0)x->0lim _ f (x)=lim (1-cos 4x)/x^(2)

for f(x) to be continuous at x=0lim _ f (x)=f (0)x->0lim _ f (x)=lim (1-cos 4x)/x^(2)x->0 x->0

for f(x) to be continuous at x=0lim _ f (x)=f (0)x->0lim _ f (x)=lim (1-cos 4x)/x^(2)x->0 x->0=lim 2 sin^(2) 2x/x^(2)

for f(x) to be continuous at x=0lim _ f (x)=f (0)x->0lim _ f (x)=lim (1-cos 4x)/x^(2)x->0 x->0=lim 2 sin^(2) 2x/x^(2)x->0

for f(x) to be continuous at x=0lim _ f (x)=f (0)x->0lim _ f (x)=lim (1-cos 4x)/x^(2)x->0 x->0=lim 2 sin^(2) 2x/x^(2)x->0=lim (2*4) sin^(2) 2x/ (2^(2) * x^(2))

for f(x) to be continuous at x=0lim _ f (x)=f (0)x->0lim _ f (x)=lim (1-cos 4x)/x^(2)x->0 x->0=lim 2 sin^(2) 2x/x^(2)x->0=lim (2*4) sin^(2) 2x/ (2^(2) * x^(2))x->0

for f(x) to be continuous at x=0lim _ f (x)=f (0)x->0lim _ f (x)=lim (1-cos 4x)/x^(2)x->0 x->0=lim 2 sin^(2) 2x/x^(2)x->0=lim (2*4) sin^(2) 2x/ (2^(2) * x^(2))x->0=8lim (sin 2x/2x)^(2)

for f(x) to be continuous at x=0lim _ f (x)=f (0)x->0lim _ f (x)=lim (1-cos 4x)/x^(2)x->0 x->0=lim 2 sin^(2) 2x/x^(2)x->0=lim (2*4) sin^(2) 2x/ (2^(2) * x^(2))x->0=8lim (sin 2x/2x)^(2)x->0

for f(x) to be continuous at x=0lim _ f (x)=f (0)x->0lim _ f (x)=lim (1-cos 4x)/x^(2)x->0 x->0=lim 2 sin^(2) 2x/x^(2)x->0=lim (2*4) sin^(2) 2x/ (2^(2) * x^(2))x->0=8lim (sin 2x/2x)^(2)x->0=8*1 [using lim sin x/x =1]

for f(x) to be continuous at x=0lim _ f (x)=f (0)x->0lim _ f (x)=lim (1-cos 4x)/x^(2)x->0 x->0=lim 2 sin^(2) 2x/x^(2)x->0=lim (2*4) sin^(2) 2x/ (2^(2) * x^(2))x->0=8lim (sin 2x/2x)^(2)x->0=8*1 [using lim sin x/x =1]x->0

for f(x) to be continuous at x=0lim _ f (x)=f (0)x->0lim _ f (x)=lim (1-cos 4x)/x^(2)x->0 x->0=lim 2 sin^(2) 2x/x^(2)x->0=lim (2*4) sin^(2) 2x/ (2^(2) * x^(2))x->0=8lim (sin 2x/2x)^(2)x->0=8*1 [using lim sin x/x =1]x->0=8

for f(x) to be continuous at x=0lim _ f (x)=f (0)x->0lim _ f (x)=lim (1-cos 4x)/x^(2)x->0 x->0=lim 2 sin^(2) 2x/x^(2)x->0=lim (2*4) sin^(2) 2x/ (2^(2) * x^(2))x->0=8lim (sin 2x/2x)^(2)x->0=8*1 [using lim sin x/x =1]x->0=8=f (0)

for f(x) to be continuous at x=0lim _ f (x)=f (0)x->0lim _ f (x)=lim (1-cos 4x)/x^(2)x->0 x->0=lim 2 sin^(2) 2x/x^(2)x->0=lim (2*4) sin^(2) 2x/ (2^(2) * x^(2))x->0=8lim (sin 2x/2x)^(2)x->0=8*1 [using lim sin x/x =1]x->0=8=f (0)=k

for f(x) to be continuous at x=0lim _ f (x)=f (0)x->0lim _ f (x)=lim (1-cos 4x)/x^(2)x->0 x->0=lim 2 sin^(2) 2x/x^(2)x->0=lim (2*4) sin^(2) 2x/ (2^(2) * x^(2))x->0=8lim (sin 2x/2x)^(2)x->0=8*1 [using lim sin x/x =1]x->0=8=f (0)=kHence, k=8

Step-by-step Explanation:

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