Question 735077: Please help me solve this question.
Let g : N -> {+-cos(x), +-sin(x)} be defined by
a)Find a description of g(n) without using the differential operator.
b)What is the 101st derivative of sinx? That is find g(101).
I have no idea where to start or how to do a). But I think once I have a) it might be easier to understand and work out b). But I thought I would still ask both. Thank you for your assistance in advance.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! Let's look at sin(x) first.
y=sin(x)
y'(x)=cos(x)
y''(x)=-sin(x)
y'''(x)=-cos(x)
y''''(x)=sin(x), so at the 4th derivative, we're back to sin(x)
n=1,5,9,13,..., derivative=cos(x)
n=2,6,10,14,..., derivative=-sin(x)
n=3,7,11,15,..., derivative=-cos(x)
n=4,8,12,16,..., derivative=sin(x)
g(101) = cos(x)
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