A heavy block of mass M hangs in equilibrium at the end of a rope of mass m and length l connected to a ceiling . Determine the tension in the rope at a distance x from the ceiling ?
The Tension T is supporting

the mass
#M# of the block 
that mass of the rope belonging to the length
#l  x# . Assuming even distribution of mass along the rope, that mass is#(l  x)/l m# This we can say that
#T(x) = g ( M + (l  x)/l m)#
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To determine the tension in the rope at a distance x from the ceiling, we can use the principle of equilibrium. The tension in the rope at that point will be equal to the weight of the block plus the tension in the portion of the rope below that point. Therefore, the tension T at a distance x from the ceiling is given by the equation:
T = Mg + (m/l) * x * g
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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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