Asked by Catherine
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/(2ãt)
s '(1) = 1/(2ã1) = 1/2
But I can't get the answer by evaluating the limit algebraically.. can someone please show me the procedure?
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/(2ãt)
s '(1) = 1/(2ã1) = 1/2
But I can't get the answer by evaluating the limit algebraically.. can someone please show me the procedure?
Answers
Answered by
Reiny
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
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
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.