Question

Find the vertical asymptotes of the following :-

a) x-1/(x²+5x+6)

b) sin (x)

c) ln(x)²

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Answer 1

Step-by-step explanation:

Given:

a) x-1/(x²+5x+6)

b) sin (x)

c) ln(x)²

To find: Vertical asymptotes of given function.

Solution:

If a function is in the form f(x)=n(x)/d(x), then put d(x)=0, the solution will be the vertical asymptotes for that function.

$a) \frac{x - 1}{ {x}^{2} + 5x + 6}$

put denominator equal to zero

${x}^{2} + 5x + 6 = 0 \\ \\ {x}^{2} + 2x + 3x + 6 = 0 \\ \\ x(x + 2) + 3(x + 2) = 0 \\ \\ (x + 3)(x + 2) = 0 \\ \\ (x + 3) = 0 \\ \\ x = - 3 \\ \\ or \\ \\ (x + 2) = 0 \\ \\ x = - 2$

The function have vertical asymptotes at x = -3 and x= -2.

b) sin(x)

The function sin x has no vertical asymptotes,since for any points it's value does not reach to infinity.

c) ln(x)²

vertical asymptotes can not be calculated for such type of function.

Hope it helps you.