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Finding the Path of a Heat-Seeking Particle In Exercises 59 and 60, find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at ( x, y) is T( x, y).
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EBK CALCULUS: EARLY TRANSCENDENTAL FUNC
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University Calculus: Early Transcendentals (3rd Edition)
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- Flux of F(x,y) = 5 x î +3 y ĵ across the circle x? + y? = 1 (anticlockwise) is - 8 T Can not find.arrow_forwardFind the linearization of the function a) z = cos(sin y – x); at (-2,0) and use it to approximate f(-1.99,0.01). 10x2 b) z = i at (4, –1) and use it to approximate f(4.01, –0.9). x-y'arrow_forwardTransient Orifice Flow: Water is discharged from a reservoir through a long pipe as shown. By neglecting the change in the level of the reservoir, the transient velocity of the water flowing from the pipe, vt), can be expressed as: - Reservoir v(t) V2gh = tanh V2gh) Pipe Where h is the height of the fluid in the 7- reservoir, L is the length of the pipe, g is the acceleration due to gravity, and t is the time elapsed from the beginning of the flow Transient Orifice Flow: Determine the helght of the fluid in the reservoir at time, t= 2.5 seconds, given that the velocity at the outfall, vt) = 3 m/s, the acceleration due to gravity, g = 9.81 m/s? and the length of the pipe to outfall, L= 1.5 meters. Reservoir v(t) V2gh = tanh 2L 2gh water Pipe Hint: Transform the equation to a function of form: fih) = 0 Solve MANUALLY using BISECTION AND REGULA-FALSI METHODS, starting at xn = 0.1, Kg =1, E = 0.001 and If(*new)l < Earrow_forward
- (ii) Let variables x, y and z be linked by the two relationships f(x, y, z) = x³y-z-1=0, g(x, y, z) = x + y² +2³ 2³-6=0. Derive conditions on the differentials dx, dy, and dz if the functions f and g are kept at these values. Show that (x, y, z) = (1, 2, 1) is a solution. Use calculus (i.e., by using the expressions for dx, dy, dz) to estimate the corresponding values of x and y when z = 1.1.arrow_forwardPls explain in detail. thxarrow_forwardReal Analysis II Please solve 1b,c&darrow_forward
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