Duplicate Question
The question on this page has been marked as a duplicate question.
Original Question
Of the infinitely many lines that are tangent to the curve y = −7 sin x and pass through the origin, there is one that has the...Asked by TayB
Of the infinitely many lines that are tangent to the curve
y = −4 sin x
and pass through the origin, there is one that has the largest slope. Use Newton's method to find the slope of that line correct to six decimal places.
y = −4 sin x
and pass through the origin, there is one that has the largest slope. Use Newton's method to find the slope of that line correct to six decimal places.
Answers
Answered by
Steve
A quick look at the graph shows that the point we want will be somewhere in the interval [pi,2pi].
The line through (0,0) and (x,-4sinx) is
y = -4sinx/x
we also know that at any point x, the slope is
y' = -4cos(x)
So, we need
-4sin(x)/x = -4cos(x)
tanx = x
So, let f(x) = tanx-x
Pick x = 4.7 (near 3pi/2, which is an asymptote) as the initial guess, and apply Newton's method to that. I get x=4.493
The line through (0,0) and (x,-4sinx) is
y = -4sinx/x
we also know that at any point x, the slope is
y' = -4cos(x)
So, we need
-4sin(x)/x = -4cos(x)
tanx = x
So, let f(x) = tanx-x
Pick x = 4.7 (near 3pi/2, which is an asymptote) as the initial guess, and apply Newton's method to that. I get x=4.493
Answered by
TayB
That's not correct Steve that's not to six decimal places like the problem says
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.