# Andy is 6 feet tall and is walking away from a street light that is 30 feet above ground at a rate of 2 feet per second. How fast is his shadow increasing in length?

Let the man be

By similar triangles:

# y/6=(x+y)/30 #

# :. 30y=6(x+y) #

# :. 30y=6x+6y #

# :. 30y-6y=6x #

# :. 24y=6x #

# :. y=1/4x #

Now,

#=> l=x+1/4x#

# :. l=5/4x#

Differentiating wrt

# (dl)/dx=5/4 #

And by the chain rule we have:

# (dl)/dt=(dl)/dx dx/dt #

# :. (dl)/dt=5/4 xx 2 #

# :. (dl)/dt=2.5 # feet/sec

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The rate of increase of Andy's shadow's length is ( \frac{5}{3} ) feet per second.

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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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