If f(x)=(2-√x+4/ sin 2x)(x≠ 0) is continuous function at x=0, then f(0) equals to

Question

If f(x)=(2-√x+4/ sin 2x)(x≠ 0) is continuous function at x=0, then f(0) equals to (A)  (1/4)  (B)  -(1/4)  (C)  (1/8)  (D)  -(1/8)

Tardigrade Admin · Accepted Answer

There are 7 letters in the word FAILURE. To include F in every 4 letters word, we first select four letters from the 7 letters of the word FAILURE such that F is included in every selection. This can be done by selecting three letters from the remaining six letters. ie, A, text I, text L, text U, text R, text E in 6C3 ways. Now there are 4 letters in each of 6C3 selections. Also every selection contains letters which can be arranged in 4! ways. Hence, the required number of four letter words =6C3× 4!=(6.5.4/3.2.1).24 =20× 24=480

Q. If $f (x) = \frac{2 - x + 4}{s i n 2 x} (x \neq = 0)$ is continuous function at $x = 0,$ then $f (0)$ equals to

$\frac{1}{4}$

$- \frac{1}{4}$

$\frac{1}{8}$

$- \frac{1}{8}$

Q. If f(x)=sin2x2−x+4​​(x=0) is continuous function at x=0, then f(0) equals to

41​

−41​

81​

−81​

Q. If $f (x) = \frac{2 - x + 4}{s i n 2 x} (x \neq = 0)$ is continuous function at $x = 0,$ then $f (0)$ equals to

$\frac{1}{4}$

$- \frac{1}{4}$

$\frac{1}{8}$

$- \frac{1}{8}$