# What is the instantaneous velocity of an object moving in accordance to # f(t)= (tlnt,e^(2t)) # at # t=2 #?

Instantaneous velocity of the object is

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To find the instantaneous velocity of an object moving according to the function ( f(t) = (t \ln t, e^{2t}) ) at ( t = 2 ), we need to differentiate the function with respect to time and then evaluate it at ( t = 2 ).

The derivative of ( f(t) = (t \ln t, e^{2t}) ) with respect to time ( t ) is ( f'(t) = (\ln t + 1, 2e^{2t}) ).

Now, we can substitute ( t = 2 ) into ( f'(t) ) to find the instantaneous velocity at ( t = 2 ):

( f'(2) = (\ln 2 + 1, 2e^{4}) )

So, the instantaneous velocity of the object at ( t = 2 ) is ( (\ln 2 + 1, 2e^{4}) ).

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When evaluating a one-sided 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 one-sided 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 one-sided 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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