9514 1404 393
Answer:
b ≈ 0.240450937397
Step-by-step explanation:
To find the y-intercept of the tangent line, you need to know ...
a) the value of y at x=3
b) the slope of the curve at x=3
__
The slope is found by differentiating the function.
y = ln(x·e^(cos(x)²)) = ln(x) +cos(x)²
Then the derivative is ...
y' = 1/x +2(-sin(x)·cos(x)) = 1/x -sin(2x)
The y-intercept is ...
b = y - x·y'
b = ln(3) +cos(3)² -3(1/3 -sin(6))
The y-intercept is ...
b = ln(3) +3·sin(6) +cos(3)² -1 ≈ 0.240450937397
