Use the limit process to find the slope of the graph of
sqrt(x + 8) at (8, 4).
2 answers
Just so you can check your work, you should come up with 1/8
slope= lim (sqrt(x+8+dx)-sqrt(x+8))/dx
multipy num/den by sqrt(x+8+dx)+sqrt(x+8)
slope= lim (x+8+dx-x-8)/(dx*(sqrt(x+8+dx)+sqrt(x+8)
slope= lim ((dx/dx)/sqrt(x+8+dx)+sqrt(x+8)
= 1/(2(sqrt(x+8))
so at x=8, slope= 1/8
multipy num/den by sqrt(x+8+dx)+sqrt(x+8)
slope= lim (x+8+dx-x-8)/(dx*(sqrt(x+8+dx)+sqrt(x+8)
slope= lim ((dx/dx)/sqrt(x+8+dx)+sqrt(x+8)
= 1/(2(sqrt(x+8))
so at x=8, slope= 1/8