Question

8. List all vertical asymptotes in the interval (0,2) for: f(x)=- 1+2 sin(x) D. x = 77 117 x 6 E -417 57 33 F. None of the above.

Answer 1

J f(3) = 1 ) 1 + 2 sinc

For vertical asymptotes we set denominator to 0

>1+ 2sinx = 0

=> 2 sinr = -1

=> sinr =

=> sinx = sin

General solution of sinx = sin b for x is

x = n1 +(-1) 6

=> r=n7+(-1)"

(-1)" => x=nn -

n=0  $=>x=-\frac{\pi}{6}$

n=1

-17 => x=- + 6

n=2

117 => r = 27 -

n=3 $=>x=3\pi-\frac{-\pi}{6}=3\pi+\frac{\pi}{6}=\frac{19\pi}{6}$

As

X€0,27

There fore

7 11 台,