Using a Function In Exercises 67 and 68, (a) find the gradient of the function at P, (b) find a unit normal
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Multivariable Calculus
- Describe the two main geometric properties of the gradient V f.arrow_forwardFind the gradient of the function at the given point. Function Point f(x, у, 2) x² + y2 + z2 (8, 7, 3) %3D Vf(8, 7, 3) = %3D Find the maximum value of the directional derivative at the given point.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_forward
- Find the gradient of the function at the given point. Function Point f(x, у, 2) x² + y? + z? (2, 7, 4) = Vf(2, 7, 4) = Find the maximum value of the directional derivative at the given point.arrow_forwardOhm's law states that the voltage drop Vacross an ideal resistor is linearly proportional to the current i flowing through the resistor as V= iR. Where R is the resistance. However, real resistors may not always obey Ohm's law. Suppose that you perform some very precise experiments to measure the voltage drop and the corresponding current for a resistor. The following results suggest a curvilinear relationship rather than the straight line represented by Ohm's law. i -1 - 0.5 - 0.25 0.25 0.5 1 V -637 -96.5 -20.25 20.5 96.5 637 Instead of the typical linear regression method for analyzing such experimental data, fit a curve to the data to quantify the relationship. Compute V for i = 0.1 using Polynomial Interpolation.arrow_forwardOhm's law states that the voltage drop Vacross an ideal resistor is linearly proportional to the current i flowing through the resistor as V= iR. Where R is the resistance. However, real resistors may not always obey Ohm's law. Suppose that you perform some very precise experiments to measure the voltage drop and the corresponding current for a resistor. The following results suggest a curvilinear relationship rather than the straight line represented by Ohm's law. i -1 - 0.5 - 0.25 0.25 0.5 1 V -637 -96.5 -20.25 20.5 96.5 637 Instead of the typical linear regression method for analyzing such experimental data, fit a curve to the data to quantify the relationship. Compute V for i = 0.1 using Newton's Divided Difference Method.arrow_forward
- Find the gradient of the function at the given point. w = x tan(y + z), (10, 5, -2) 2, Vw(10, 5, -2) = tan(3), 10 sec-(3), 10 sec-(3)arrow_forwardgn) / Final Exam Sem2, 2020-2021 Part 2 a) Find the points at which the tangent line to the graph of function f(x)=2x-24x+6 has slope equal to 0arrow_forwardI would need help with a, b, and c as mention below. (a) Find the gradient of f.(b) Evaluate the gradient at the point P.(c) Find the rate of change of f at P in the direction of the vector u.arrow_forward
- Find the directional derivative of the function at point P in the direction of Q. f(x, у, z) P(2, 1, –1), Q(-1, 8, 0) x + zarrow_forwardHeat transfer Fourier’s Law of heat transfer (or heat conduction) states that the heat flow vector F at a point is proportional to the negative gradient of the temperature; that is, F = -k∇T, which means that heat energy flows from hot regions to cold regions. The constant k > 0 is called the conductivity, which has metric units of J/(m-s-K). A temperature function for a region D is given. Find the net outward heat flux ∫∫S F ⋅ n dS = -k∫∫S ∇T ⋅ n dS across the boundary S of D. In some cases, it may be easier to use the Divergence Theorem and evaluate a triple integral. Assume k = 1. T(x, y, z) = 100e-x2 - y2 - z2; D is the sphere of radius a centered at the origin.arrow_forwardHeat transfer Fourier’s Law of heat transfer (or heat conduction) states that the heat flow vector F at a point is proportional to the negative gradient of the temperature; that is, F = -k∇T, which means that heat energy flows from hot regions to cold regions. The constant k > 0 is called the conductivity, which has metric units of J/(m-s-K). A temperature function for a region D is given. Find the net outward heat flux ∫∫S F ⋅ n dS = -k∫∫S ∇T ⋅ n dS across the boundary S of D. In some cases, it may be easier to use the Divergence Theorem and evaluate a triple integral. Assume k = 1. T(x, y, z) = 100 + x2 + y2 + z2;;D = {(x, y, z): 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, 0 ≤ z ≤ 1}arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage