Step 1 From the text, the slope of the tangent line to the function f(x) is lim f (x + h) - f(x). Substituting h - 0 h f(x) = 5vx into this formula and multiplying by the conjugate divided by the conjugate, we have the following. lim f ( x + h ) - f (x ) xth htx - 5Vx = lim h - 0 h h - h lim xth 5vh h+x - 5V x X 5vh+x+5Vx h - 0 h 5 \\ x + h + 5 \\x Step 2 Multiplying out the numerator and then simplifying, we have the following. 5 v x + h - 5Vx/ 5Vx+ h+ 5Vx 5 5 lim lim h - 0 5v xth+ 5vx h - 0 Vxth + vx Vhte+vi Step 3 Taking the limit by direct substitution and simplifying, we have the following. 5 5 lim h-ovxth+vx x + + Vx X