Find the indicated derivatives.
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- make v the subject 1/f=1/u+1/varrow_forwardREFER TO IMAGEarrow_forwardA function f and a point P are given. Let 9 correspond to the direction of the directional derivative. Complete parts a. through e. f(x,y) = In (1 +6x² +5y²), P ( 2₁ -√²) a. Find the gradient and evaluate it at P. 4√2 5 The gradient at P is 12 25 (...) b. Find the angles 9 (with respect to the positive x-axis) between 0 and 2 associated with the directions of maximum increase, maximum decrease, and zero change. What angles are associated with the direction of maximum increase? (Type your answer in radians. Type an exact answer in terms of . Use a comma to separate answers as needed.)arrow_forward
- Define the relationship between x and yarrow_forwardDetermine whether the functions y, and y, are linearly dependent on the interval (0,1). y1 =sint cos t, y, = 5 sin 2t Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. Since y, = y, on (0,1), the functions are linearly dependent on (0,1). (Simplify your answer.) O B. Since y, =O2 on (0,1), the functions are linearly independent on (0,1) (Simplify your answer.) O C. Since y, is not a constant multiple of y, on (0,1), the functions are linearly independent on (0,1). O D. Since y, is not a constant multiple of y, on (0,1), the functions are linearly dependent on (0,1).arrow_forwardFind f, and f and evaluate each at the given point. fox, v) = arctan(). (2, -2) %3D f,(x, y) = %3D fyx, v) = %3D 5,(2, -2) = 2, -2) =arrow_forward
- Determine whether the functions y, and y, are linearly dependent on the interval (0,1). V=1-2 sin t, y2 = 12 cos 2t Select the correct choice below and, if necessary, fill in the answer boX within your choice. CA Since y,= ]y on (0,1), the functions are linearly dependent on (0,1). (Simplify your answer ). OB. Since y = ( )y, on (0,1), the functions are linearly independent on (0,1). (Simplify your answer) OC. Since y, is not a constant multiple of y, on (0 1). the functions are linearly independent on (0,1) OD. Since y, is not a constant multiple of y, on (0,1), the functions are linearly dependent on (0, 1). 73°F Sunnyarrow_forwardhelp with 6arrow_forwardA hollow steel ball weighing 4 pounds is suspended from a spring. This stretches the spring feet. The ball is started in motion from the equilibrium position with a downward velocity of 4 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second) Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t. (Note that the positive direction is down.) Take as the gravitational acceleration 32 feet per second per second. y =arrow_forward
- Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q corresponds to t = 1.) P(-9, -2, -1), Q(−4, −8, −9) r(t) = Represent the line segment from P to Q by a set of parametric equations. (Enter your answers as a comma-separated list of equations.) Your answer cannot be understood or graded. More Informationarrow_forwardE.g. Let f(x, y) = x² − 2xy + y². The graph and contour diagram of ƒ is given below right. Compute Vf at the points: (0,0), (1, 1), (−1, 1), (1,−1), (2,0), and (0,2). Sketch each Vfp on the axes below left. What is the graphical meaning of Vfp? -1 1 -1 -2 1 2 1.0 4 0.5 y 0.0 -0.5 -1.0 2 0 -1.0 -1.0 -0.5 0.0 x -0.5 0.5 0.0 x 1.0 0.5 -0.5 1.0 70.9 -1.0 1.0 0.5arrow_forwardD) Consider a function f(S,v) of two variables, S and v. Assume that for S-103 and -0.1 we have the following numerical values for f(S,v) and its derivatives: f(S,v) = 2.3 Of(s, v) = 0.6 as 82f(S,v) =2.0 852 Of(S,v) = 0.75 θυ Estimate the value of f(Sv) when S-103.5arrow_forward
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