A software engineer is working on a project that involves developing an algorithm for a self$-$driving

car. The algorithm needs to detect the slope of the road at any given point to adjust the car's

speed and direction. The road is represented by the curve,

$y=\sqrt[\phantom{2}]{5-x^2}$

Use the limit definition of the derivative to calculate the equation of the straight line tangent to the

curve, $y=\sqrt[\phantom{2}]{5-x^2}$ at $x=1.$ Show all your calculations.