Question

f(x) = tan5x/sin2x , x is not equal to "0" and k , x is equal to "0".........function is continuous at x=0......find the value of k

Answer 1

Step-by-step explanation:

$Identity:x </p><p>3</p><p> +y </p><p>3</p><p> +z </p><p>3</p><p> −3xyz=(x+y+z)(x </p><p>2</p><p> +y </p><p>2</p><p> +z </p><p>2</p><p> −xy−yz−zx)</p><p>x+y+z=1,xy+yz+zx=−1,xyz=−1</p><p>puttingvaluesweget</p><p>x </p><p>3</p><p> +y </p><p>3</p><p> +z </p><p>3</p><p> −3(−1)=(1)(x </p><p>2</p><p> +y </p><p>2</p><p> +z </p><p>2</p><p> +1)</p><p>x </p><p>3</p><p> +y </p><p>3</p><p> +z </p><p>3</p><p> +3=x </p><p>2</p><p> +y </p><p>2</p><p> +z </p><p>2</p><p> +1</p><p>x </p><p>3</p><p> +y </p><p>3</p><p> +z </p><p>3</p><p> =x </p><p>2</p><p> +y </p><p>2</p><p> +z </p><p>2</p><p> +1−3</p><p>x </p><p>3</p><p> +y </p><p>3</p><p> +z </p><p>3</p><p> =x </p><p>2</p><p> +y </p><p>2</p><p> +z </p><p>2</p><p> −2....(1)</p><p>now</p><p>(x+y+z) </p><p>2</p><p> =x </p><p>2</p><p> +y </p><p>2</p><p> +z </p><p>2</p><p> +2(xy+yz+xz)</p><p>(1) </p><p>2</p><p> =x </p><p>2</p><p> +y </p><p>2</p><p> +z </p><p>2</p><p> +2(−1)</p><p>1=x </p><p>2</p><p> +y </p><p>2</p><p> +z </p><p>2</p><p> −2</p><p>x </p><p>2</p><p> +y </p><p>2</p><p> +z </p><p>2</p><p> =2+1</p><p>x </p><p>2</p><p> +y </p><p>2</p><p> +z </p><p>2</p><p> =3</p><p>putinequation(1)</p><p>x </p><p>3</p><p> +y </p><p>3</p><p> +z </p><p>3</p><p> =3−2</p><p>x </p><p>3</p><p> +y </p><p>3</p><p> +z </p><p>3</p><p> =1$

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