Question

Use the properties of limits to help decide whether the limit exists.find its value. limx^2 5x-36/x^2-16

Answer 1

The value of limit =
`(13)/(8)`

Explanation:

Explanation:-

Given
`\lim_(x \to 4) (x^(2)+5 x-36 )/(x^(2)-16 )`

=
`\lim_(x \to 4) (x^(2)+9 x-4 x-36 )/((x-4)(x+4) )`

=
`\lim_(x \to 4) ((x(x-4)+9(x-4) )/((x-4)(x+4) )`

=
`\lim_(x \to 4) (((x-4)(x+9))/((x-4)(x+4) )`

=
`(4+9)/(4+4)`

=
`(13)/(8)`

Hence the limit exists and The value of limit =
`(13)/(8)`