Evaluating a Line
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Calculus: Early Transcendental Functions
- Consider the complex function f(z) = . Describe the level curves Zarrow_forwardUse Green's Theorem to evaluate f, F •dr. (Check the orientation of the curve before applying the theorem.) F(x, y) = (y cos x xy sin x, xy + x cos x), C is the triangle from (0, 0) to (0, 4) to (2, 0) to (0, 0)arrow_forward(iii) Use Green's Theorem to evaluate F. dr. (Check the orientation of the curve before applying the theorem.) - F(x, y) = (y cos x − xy sin x, xy + x cos x), C is the triangle from (0,0) to (0,4) to (2,0) to (0,0).arrow_forward
- Evaluate | exp(-2²)dx, using an iterated integral and polar coordinates.arrow_forwardConsider the function r(t) = (2 cos t)i + (8 sin t)j. Find all the points on the function at which r and r' are orthogonal.arrow_forwardCalculate the line integral of the vector field F = (y, x,x² + y² ) around the boundary curve, the curl of the vector field, and the surface integral of the curl of the vector field. The surface S is the upper hemisphere x² + y + z? = 25, z 2 0 oriented with an upward-pointing normal. (Use symbolic notation and fractions where needed.) F. dr = curl(F) =arrow_forward
- Find the points of intersection between r =2cos20 and r = 1-cosearrow_forwarda) sketch the curves of f(x) and g(x) in the same plane b) calculate the area covered by the two equationsarrow_forwardStokes' Theorem (1.50) Given F = x²yi – yj. Find (a) V x F (b) Ss F- da over a rectangle bounded by the lines x = 0, x = b, y = 0, and y = c. (c) fc ▼ x F. dr around the rectangle of part (b).arrow_forward
- Displacement d→1 is in the yz plane 62.8 o from the positive direction of the y axis, has a positive z component, and has a magnitude of 5.10 m. Displacement d→2 is in the xz plane 37.0 o from the positive direction of the x axis, has a positive z component, and has magnitude 0.900 m. What are (a) d→1⋅d→2 , (b) the x component of d→1×d→2 , (c) the y component of d→1×d→2 , (d) the z component of d→1×d→2 , and (e) the angle between d→1 and d→2 ?arrow_forwardUsing the Hough transform i) Develop a general procedure for obtaining the normal representation of a line from its slope-intercept form, y = ax + b. ii) Find the normal representation of the line y = – 2x + 1.arrow_forwardThe position vector r describes the path of an object moving in the xy-plane. Position Vector Point r(t) = 4 cos ti + 4 sin t (2V2,2V2) (a) Find the velocity vector v(t), speed s(t), and acceleration vector a(t) of the objeot. v(t) s(t) = a(t) = (b) Evaluate the velocity vector and acceleration vector of the object at the given point.arrow_forward
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