Question

Hello I'm reposting this question because right now it's at the bottom and I don't think I will get an answer.

Assume that the follwing function gives the position of an object at time t. Find the velocity indicated by setting up and evaluating a limt algebraically.
s(t) = ãt, Find v(1).


I know that the answer is 1/2 because
s(t) = ãt = t(1/2)
s '(t) = (1/2)t^(-1/2) = 1/(2ãt)
s '(1) = 1/(2ã1) = 1/2

But I can't get the answer by evaluating the limit algebraically.. can someone please show me the procedure?

Answer 1

let s(t) = √t
then
derivative = Limit (√(1+h) - √1)/h as h --> 0
= Lim (√(1+h) - √1)/h * (√(1+h) + 1)/(√(1+h) + 1)
= lim (1+h - 1)/(h(√(1+h) + 1))
= lim h/(h(√(1+h) + 1))
= lim 1/(√(1+h) + 1) , as h --> (in each line above)
= 1/(√1 + 1) = 1/2