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The position of an object moving along a line is given by #p(t) = 2t - cos(( pi )/4t) #. What is the speed of the object at #t = 7 #?

Answer 1

Leo Abeyta

#v(7)=(16-sqrt2 pi)/8#

#v(t)=d/(d t) p(t)#

#v(t)=d/(d t)(2t-cos(pi/4t))#

#v(t)=2+pi/4sin(pi/4t)#

#v(7)=2+pi/4sin(pi/4*7)#

#v(7)=2+pi/4*(-sqrt2/2)#

#v(7)=2-(sqrt2pi)/8#

#v(7)=(16-sqrt2 pi)/8#

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Answer 2

Charles Aeschliman

To find the speed of the object at t = 7, differentiate the position function with respect to time, and then substitute t = 7 into the derivative.

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Answer from HIX Tutor

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.