Question

I have a calculus question about limit functions. Pic included.

Answer 1

Based on the results above, the slope of the tangent line to the curve at P(25,10) is 0.1.

Explanation:

P(25, 10) lies on the curve:

`y=√(x)+5`

Q is the point (x, √x+5).

For any value of x, the slope of the secant line PQ is determined using the formula:

`\text{ Slope of secant PQ}=((√(x)+5)-10)/(x-25)`

(a)When x=25.1

`\text{Slope of secant PQ}=((√(25.1)+5)-10)/(25.1-25)=0.0999`

(b)When x=25.01

`\text{Slope of secant PQ}=((√(25.01)+5)-10)/(25.01-25)=0.09999`

(c)When x=24.9

`\text{Slope of secant PQ}=((√(24.9)+5)-10)/(24.9-25)=0.1001`

(d)When x=24.99

`\text{Slope of secant PQ}=((√(24.99)+5)-10)/(24.99-25)=0.10001`

Based on the results above, the slope of the tangent line to the curve at P(25,10) is 0.1.