Chapter 7: Q12E (page 422)
What is a direction field for the differential equation \(y' = F(x,y)?\)
A two-dimensional graph depicting the slopes of potential solution curves at \((x,y)\)
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Graph the region between the curves and use your calculator to compute the area correct to five decimal places.
\(y = \frac{2}{{1 + {x^4}}},\quad y = {x^2}\)
Find the area of the shaped region.
Sketch the region enclosed by the given curves and find its area.
Sketch the region enclosed by the given curves.
\(12. y = {x^2},\quad y = 4x - {x^2}\)
Find the area of the region enclosed by the parabola\(y = {x^2}\)and the tangent line to this parabola at\(\left( {{\bf{1}},{\bf{1}}} \right)\), and the\(x - \)axis.
A cross-section of an airplane wing is shown. Measurements of the height of the wing, in centimetres, at 20 -centimetre intervals are 5.8,20.3,26.7,29.0,27.6,27.3,23.8, 20.5,15.1,8.7 and 2.8.
Use Simpson's Rule to estimate the area of the wing's cross-section.
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