For #f(t)= ( t2, sqrtt t )# what is the distance between #f(0)# and #f(1)#?
1
These two points lie in a straight line do distance between the points = 1
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To find the distance between ( f(0) ) and ( f(1) ) for the function ( f(t) = (t2, \sqrt{t}  t) ):

Calculate ( f(0) ): [ f(0) = (0  2, \sqrt{0}  0) = (2, 0) ]

Calculate ( f(1) ): [ f(1) = (1  2, \sqrt{1}  1) = (1, 0) ]

Use the distance formula: [ \text{Distance} = \sqrt{(x_2  x_1)^2 + (y_2  y_1)^2} ]

Plug in the values: [ \text{Distance} = \sqrt{(1  (2))^2 + (0  0)^2} = \sqrt{1^2 + 0^2} = \sqrt{1} = 1 ]
So, the distance between ( f(0) ) and ( f(1) ) is 1 unit.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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