Problem 1E: Find an equation of the tangent plane to the given surface at the specified point. z=2x2+y25y,... Problem 2E: Find an equation of the tangent plane to the given surface at the specified point. z=(x+2)22(y1)25,... Problem 3E: Find an equation of the tangent plane to the given surface at the specified point. z=exy, (2,2,1) Problem 4E: Find an equation of the tangent plane to the given surface at the specified point. z=x/y2, (4,2,1) Problem 5E: Find an equation of the tangent plane to the given surface at the specified point. z=xsin(x+y),... Problem 6E: Find an equation of the tangent plane to the given surface at the specified point. z=ln(x2y),... Problem 7E Problem 8E Problem 9E: Draw the graph of f and its tangent plane at the given point. Use your computer algebra system both... Problem 10E Problem 11E: Explain why the function is differentiable at the given point. Then find the linearization L(x,y) of... Problem 12E: Explain why the function is differentiable at the given point. Then find the linearization L(x,y) of... Problem 13E Problem 14E: Explain why the function is differentiable at the given point. Then find the linearization L(x,y) of... Problem 15E: Explain why the function is differentiable at the given point. Then find the linearization L(x,y) of... Problem 16E: Explain why the function is differentiable at the given point. Then find the linearization L(x,y) of... Problem 17E: Verify the linear approximation at (0,0). excos(xy)x+1 Problem 18E: Verify the linear approximation at (0,0). 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 linear... Problem 20E: Find the linear approximation of the function f(x,y)=1xycosy at (1,1) and use it to approximate... Problem 21E: Find the linear approximation of the function f(x,y,z)=x2+y2+z2 at (3,2,6) and use it to approximate... 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. z=e2xcos2t Problem 26E: Find the differential of the function. u=x2+3y2 Problem 27E: Find the differential of the function. m=p5q3 Problem 28E: Find the differential of the function. T=v1+uvw Problem 29E Problem 30E: Find the differential of the function. L=xzey2z2 Problem 31E Problem 32E 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 Problem 38E: The pressure, volume, and temperature of a mole of an ideal gas are related by the equation... Problem 39E: If R is the total resistance of three resistors, connected in parallel, with resistances R1,R2,R3,... Problem 40E: A model for the surface area of a human body is given by S=0.1091w0.425h0.725, where w is the weight... Problem 41E: In Exercise 14.1.39 and Example 14.3.3, the body mass index of a person was defined as B(m,h)=m/h2,... Problem 42E Problem 43E: Show that the function is differentiable by finding values of 1 and 2 that satisfy Definition 7.... Problem 44E: Show that the function is differentiable by finding values of 1 and 2 that satisfy Definition 7.... Problem 45E Problem 46E format_list_bulleted