Question

`lim_(theta → -pi/4) (cos theta + sin theta)/(theta + pi/4)` =

Options

• 0

• 1

• `sqrt2`

• `1"/"sqrt2`

Answer 1

`bbsqrt2`

Explanation:

Put `theta + pi/4 = h` or `theta = -pi/4 + h`

`lim_(h→0) (cos(pi/4 - h) - sin(pi/4 - h))/h`

= `lim_(h→0) (cos(pi/4 - h)-cos(pi/4 + h))/h`

= `lim_(h→0) (2 sin  pi/4. sin h)/h`

= `sqrt2`