Calculus problem: voltage across plates of charging capacitor varies with time according to v=10(1-e^{-0.25t})

[Smykel]

I have a problem with one question:

I can do a and c, but I am not sure when it comes to point B. Below is my solution for point C so I if some can have a look if that is also OK.
View attachment maths 5.jpg

 

[mario99]

I have a problem with one question:
View attachment 37198
I can do a and c, but I am not sure when it comes to point B. Below is my solution for point C so I if some can have a look if that is also OK.
View attachment 37199

Draw the graph of [imath]\displaystyle v = 10\left(1 - e^{-0.25t}\right)[/imath], then find the point when the time is [imath]\displaystyle t = 2.7[/imath] s. Draw a tangent line on that point, and try to approximate its slope by [imath]\displaystyle \frac{\Delta v}{\Delta t}[/imath].


The solution for (c) simply, find [imath]\displaystyle \frac{dv}{dt}[/imath], then substitute [imath]\displaystyle t = 2.7[/imath] s. Your solution is chaos