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March 2, 2015

March 2, 2015

Posted by **Catherine** on Thursday, February 17, 2011 at 10:25pm.

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) = t, Find v(1).

I know that the answer is 1/2 because

s(t) = t = t(1/2)

s '(t) = (1/2)t^(-1/2) = 1/(2t)

s '(1) = 1/(21) = 1/2

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

- Calculus Please Help -
**Reiny**, Thursday, February 17, 2011 at 11:03pmlet 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

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