Need help with questions A, B, and C.
1 answer:
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Answer:
-1
Step-by-step explanation:
The expression evaluates to the indeterminate form -∞/∞, so L'Hopital's rule is appropriately applied. We assume this is the common log.
d(log(x))/dx = 1/(x·ln(10))
d(log(cot(x)))/dx = 1/(cot(x)·ln(10)·(-csc²(x)) = -1/(sin(x)·cos(x)·ln(10))
Then the ratio of these derivatives is ...
lim = -sin(x)cos(x)·ln(10)/(x·ln(10)) = -sin(x)cos(x)/x
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At x=0, this has the indeterminate form 0/0, so L'Hopital's rule can be applied again.
d(-sin(x)cos(x))/dx = -cos(2x)
dx/dx = 1
so the limit is ...
lim = -cos(2x)/1
lim = -1 when evaluated at x=0.
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I find it useful to use a graphing calculator to give an estimate of the limit of an indeterminate form.
The position vector of P and Q is P = ( 6 i -3j +9k ) , Q = ( 3i -6 j -3k) , the coordinates of R is ( 5 , -4 , 2)
<h3>What is a vector ?</h3>A vector is an object with both mass and magnitude.
It is given that
The coordinates of
P (6, -3,9 ) and Q (3, -6, -3)
point R divides line PQ internally in the ratio 1:2.
The position vectors of P, Q and R is given by p, q and r respectively.
The position vector of P and Q in terms of i, j, k is is
P = ( 6 i -3j +9k ) , Q = ( 3i -6 j -3k)
The magnitude of P =
|p| = 11.224
The magnitude of Q =
|q| = 7.348
The coordinate of R is
if a point (x,y,z) divides the line joining the points (x₁,y₁) ) and (x₂ ,y₂) in the ratio m:n, then
( x, y, z ) =
The m : n = 1 : 2
(x,y,z) =
(x,y,z) = 5 , -4 , 2
Therefore the coordinates of R is ( 5 , -4 , 2)
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