Problem 1E: Find an equation of the tangent plane to the given surface at the specified point. 1. z = 2x2 + y2 ... Problem 2E: Find an equation of the tangent plane to the given surface at the specified point. 2. z = (x + 2)2 ... Problem 3E: Find an equation of the tangent plane to the given surface at the specified point. 3. z = exy, (2,... Problem 4E: Find an equation of the tangent plane to the given surface at the specified point. 4. z = x/y2, (4,... Problem 5E: Find an equation of the tangent plane to the given surface at the specified point. 5. z = x sin(x +... Problem 6E: Find an equation of the tangent plane to the given surface at the specified point. 6. z = ln(x 2y),... Problem 7E Problem 8E Problem 11E: Explain why the function is differentiable at the given point. Then find the linearization L(x, y)... Problem 12E: Explain why the function is differentiable at the given point. Then find the linearization L(x, y)... Problem 13E: Explain why the function is differentiable at the given point. Then find the linearization L(x, y)... Problem 14E: Explain why the function is differentiable at the given point. Then find the linearization L(x, y)... Problem 15E: Explain why the function is differentiable at the given point. Then find the linearization L(x, y)... Problem 16E: Explain why the function is differentiable at the given point. Then find the linearization L(x, y)... Problem 17E: Verify the linear approximation at (0, 0). 17. ex cos(xy) x + 1 Problem 18E: Verify the linear approximation at (0, 0). 18. y1x+1x+y1 Problem 19E: Given that f is a differentiable function with f(2, 5) = 6, fx(2, 5) = 1, and fy(2, 5) = -1, use a... Problem 20E: Find the linear approximation of the function f(x, y) = 1 xy cos y at (1, 1) and use it to... Problem 21E: Find the linear approximation of the function f(x,y,z)=x2+y2+z2 at (3, 2, 6) and use it to... Problem 22E: The wave heights h in the open sea depend on the speed v of the wind and the length of time t that... Problem 23E Problem 24E Problem 25E: Find the differential of the function. 25. z = e2x cos 2t Problem 26E: Find the differential of the function. 26. u=x2+3y2 Problem 27E: Find the differential of the function. 27. m = p5q3 Problem 28E: Find the differential of the function. 28. T=v1+uvw Problem 29E: Find the differential of the function. 29. R = 2 cos Problem 30E Problem 31E Problem 32E: If z = x2 xy + 3y2 and (x, y) changes from (3, 1) to (2.96, 0.95), compare the values of z and dz. Problem 33E: The length and width of a rectangle are measured as 30 cm and 24 cm, respectively, with an error in... Problem 34E: Use differentials to estimate the amount of metal in a closed cylindrical can that is 10 cm high and... Problem 35E: Use differentials to estimate the amount of tin in a closed tin can with diameter 8 cm and height 12... Problem 36E Problem 37E: The tension T in the string of the yo-yo in the figure is T=mgR2r2+R2 where m is the mass of the... Problem 38E: The pressure, volume, and temperature of a mole of an ideal gas are related by the equation PV =... Problem 39E: If R is the total resistance of three resistors, connected in parallel, with resistances R1, R2 R3... Problem 40E Problem 41E Problem 42E: Suppose you need to know an equation of the tangent plane to a surface S at the point P(2, 1,3). You... Problem 43E Problem 44E Problem 45E Problem 46E: (a) The function f(x,y)={xyx2+y2if(x,y)(0,0)0if(x,y)=(0,0) was graphed in Figure 4. Show that fx(0,... format_list_bulleted