7-5-49 L'Hopital's rule
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If we use Lopital's rule to find the following limit, the limit
as Theta goes to zero of seven sine Theta, cosine Theta minus
Theta over tangent Theta minus Theta.
So we're going to use the product rule on the top.
So we get 7 cosine Theta times cosine Theta -7 sine Theta, sine
Theta -1 over the derivative of tangent Theta with secant
squared Theta.
And then -1 when Theta goes to 0, we can see we get seven
times.
Cosine of 0 is 1, cosine of 0 is 1 - 7 sine of 0 is 0.
So zero times anything goes away and then -1 the secant squared
of zero.
Well, if we're coming to 0 for secant on right or left, it's
going to be one -1 and it's going to be one that's from the
positive side.
So if we have 1 + 1 from the positive side -1 we really are
getting something really, really small.
Because remember, it's what's happening when we approach 0,
not when we're at 0.
So we're going to get six over something really, really small,
which is going to be something very big.
S Our answer should be Infinity.