so i am trying to solve tangent line slopes where i have y2-y1/x2-x1.......but the next part of the problem is asking me to estimate the value that the corresponding slopes approach. How do i go about that? List of m=(-0.0773,-0.0708,-0.0656,-0.068,-0.064, 0.06)............Here's the whole question is anyone feels like solving by the time anyone responds i'll probably be asleep............1. Consider finding the equation of the line tangent to the graph of the equation f(x)=1/sqrt.(x) at x=4: (my answer f(4)= 1/sqrt.(4)=1/2......a. find the point of tangency: (my answer (4,1/2))........b. Find the slope of each line that pass through the point of tangency and the point with the x-coordinate given below. (Round slopes to 4 decimal places.)
| x= | m=(my answers) |
| 3 | -0.0773 |
| 3.5 | -0.0708 |
| 3.75 | -0.0656 |
| 3.9 | -0.068 |
| 3.95 | -0.064 |
| 3.99 | -0.06 |
As x approaches 4, estimate the value that the corresponding sples approach:____________..........c.write the equation of the tangent line:____________________
email me at EMB31e@gmail.com if anyone can help
+130516 Here are my answers
x = 3 mine agrees with yours
x = 3.5 m = [1/2 - 1/sqrt(3.5)] / [4 - 3.5 ] = -.0690
x = 3.75 m = [1/2 - 1/sqrt(3.75)] / [ 4 - 3.75] = -.0656
x = 3.9 m = [1/2 - 1/sqrt(3.9)] / [ 4 - 3.9] = -.0637
x = 3.95 m = [1/2 - 1/sqrt(3.95)] / [ 4 - 3.95] = -.0631
x = 3.99 m = [1/2 - 1/sqrt(3.99)] / [ 4 - 3.99] = -.0626
It appears that as x → 4, the slope is about -.0626
If you haven't had Calculus.....hide your eyes......but the exact slope at x = 4 is given by :
(-1/2)(x)-3/2 = (-1/2)(4)-3/2 = -.0625
The equation of the tangent line is given by :
y - (1/2) = -.0625(x - 4)
y = -,0625x + 1/4 + 1/2
y = -.0625x + 3/4
Here's a graph of the function and the tangent line.....https://www.desmos.com/calculator/ygyhq8trhm
