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Sketching a Contour Map In Exercises 51-58, describe the level curves of the function. Sketch a contour map of the surface using level curves for the given c-values.
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Chapter 13 Solutions
Bundle: Calculus: Early Transcendental Functions, Loose-leaf Version, 6th + WebAssign Printed Access Card for Larson/Edwards' Calculus: Early Transcendental Functions, 6th Edition, Multi-Term
- d) The drag coefficient in aircraft industry affected by some parameters which are the speed of plane (v), the plane length (L), the air density (p), the air dynamic viscosity (u), and speed of sound (a). By using dimensional analysis, identify two non-dimension numbers in which the drag coefficient is a function of them and explain how these two will effect on drag coefficient.arrow_forwardChange of variables Consider the parameterized curvesr(t) = ⟨ƒ(t), g(t), h(t)⟩ and R(t) = ⟨ƒ(u(t)0, g(u(t)), h(u(t))⟩, where ƒ, g, h, and u are continuously differentiable functions and u has an inverse on [a, b].a. Show that the curve generated by r on the intervala ≤ t ≤ b is the same as the curve generated by R onu-1(a) ≤ t ≤ u-1(b) (or u-1(b) ≤ t ≤ u-1(a)).b. Show that the lengths of the two curves are equal.(Hint: Use the Chain Rule and a change of variables in the arc length integral for the curve generated by R.)arrow_forwardGeometry Review Worksheet A (1) Refer to the figure to the right , given DE || BC. (a) AD = 7, BD= 3, DE = 6 Find: BC_ (b) AD = 3, BD = 5 , AE = 4 Find: CE E (c) AD = 4, AB = 10 , BC = 25 Find: DE (d) AD = (x –1), BD = 5 , AE = 1, CE = (x +3), DE = (2x + 1) Find: x , BC_ B (e) AD = 2x , BD = (x + 3), AE = (4x – 1), СЕ 3 5х , ВС - (6х + 2) Find: х. DE (2) Refer to the figure to the right, Z1 = 2. (a) AC = 6 , BC = 8 , BD = 5 Find: AD (b) AB = 10 , AC = 4 , BC = 8 Find: AD (c) AC = 3 , AD = (x – 4) , BC = x , BD = 4 Find: BC A D В (3) Given: ABCD is a parallelogram, sides as (4) Given: The figure below, 1||m||n marked. 12 1 10 8 x + 2 D C. Find: BE_ СЕ CF Find: xarrow_forward
- x + y (2) Sketch the level curves for the fuction f(r, y) and the values -2,-1, 1,2 I -Y Describe the level curve for a general value c E R.arrow_forwardarctan y Let f(x;y) =- 2+x Determine f. and f,.arrow_forwardUsing Green's theorem find the value of f F.drWhere F(x,y) = (e* – y³)i + (cosy + x³)j and C is the closed triangle bounded by the lines x = 0, y = 0 and x + y = 2.arrow_forward
- Slopes and Tangent Lines In Exercises 1-4, use the grid and a straight edge to make a rough estimate of the slope of the curve (in y-units per x-unit) at the points P, and P.. 3. 4. AL 1. 2. P. toarrow_forwardThe level curves are O The graph of a two variable function in 3D O A set of curves tangent to the gradient of a function A set of plane curves that describe a contour map of a graph in 3D O A space curve in 3Darrow_forwardAnalyze and sketch a graph of the function. Find any intercepts, relative extrema, points of inflection, and asymptotes. (If an answer does not exist, enter DNE.) y = x + 75 Intercept (х, у) %3 0,0 (х, у) %3 (0,0 relative minimum relative maximum (х, у)%3 dne points of inflection (x, y) = (smaller x-value) (х, у) %3D (larger x-value) Find the equation of the asymptote.arrow_forward
- Contour map of f(x, y). Is fa positive or negative at B?arrow_forwardAssessment Consider the following function: f (x) = = x* + 2x' + 8x + 5x Employ parabolic interpolation to find the maximum of the function and search from x, = -2, x2 = -1, x3 = 1. %3D %3Darrow_forwardThe figure shows graphs of r', the rate of change of revenue, and c', the rate of change of costs (both in thousand dollars per thousand dollars of capital investment) associated with the production of solid wood furniture as functions of x, the amount (in thousand dollars) invested in capital. The area of the shaded region is 13.26. y thousand dollars per thousand dollars c" x thousand dollars 1.5 5.5 (a) Write a sentence of interpretation for the area of the region shaded in the figure. As capital investment increased from $1.5 thousand to $5.5 thousand, profit increased by $ thousand. (b) Write an equation for the area of the shaded region. ---Select--- ---Select--- dx = 1.5arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage