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**1. Problem statment**

Q. Use limit to find the instantaneous velocity at time t if the postition is p(t) at time t.

p(t) = t + (1/t) at x = t

2. Homework Equations

(Sorry dashes are in there to keep everything where it should be. I don't know how to make fractions in this and it was deleting spaces.)

lim------f ( x+h ) - f (x)

x->0 ---_____________ (instantaneous velocity)

------------------h

Q. Use limit to find the instantaneous velocity at time t if the postition is p(t) at time t.

p(t) = t + (1/t) at x = t

2. Homework Equations

(Sorry dashes are in there to keep everything where it should be. I don't know how to make fractions in this and it was deleting spaces.)

lim------f ( x+h ) - f (x)

x->0 ---_____________ (instantaneous velocity)

------------------h

## The Attempt at a Solution

(Sorry dashes are in there to keep everything where it should be. I don't know how to make fractions in this and it was deleting spaces.)

-First I plugged in t

**lim------f ( t+h ) - f (t)**

x->0---_____________

----------------h

x->0---_____________

----------------h

**-Then I plugged in what the equation gives you when you plug those in**

**lim------[( t + h ) + (1 / ( t + h )] - [ t + ( 1 / t) ]**

--------------------------------h

-simplified it**______________________________****x->0---**--------------------------------h

-simplified it

**[/B]**

**lim-----t + h + ( 1 / t ) + ( 1 / h ) - t + ( 1 / t )--------lim-----h + ( 1 / h )**

-------------------------h-----------------------------------------------------h

- so then to get the fraction out of the numerator i multiplied numerator and denominator by h/h giving me

lim----h^2 + 1

-----------h^2

-this is where im stuck. I'm pretty sure I cant stop here because if I plug in zero then I get DNE. But I'm also not sure if I messed up somewhere or just dont know something

**_____________________________ =****x->0 -****---___________****x->0**-------------------------h-----------------------------------------------------h

- so then to get the fraction out of the numerator i multiplied numerator and denominator by h/h giving me

lim----h^2 + 1

**_______****x->0 -**-----------h^2

-this is where im stuck. I'm pretty sure I cant stop here because if I plug in zero then I get DNE. But I'm also not sure if I messed up somewhere or just dont know something