Problem 1QCE: Assume that fx,y is differentiable at x0,y0 and let f denote the change in f from its value at x0,y0... Problem 2QCE: Compute the differential of each function. az=xey2bw=xsinyz Problem 3QCE: If f is differentiable at x0,y0, then the local linear approximation to f at x0,y0 is Lx=. Problem 4QCE: Assume that f1,2=4 and fx,y is differentiable at 1,2 with fx1,2=2 and fy1,2=3. Estimate the value of... Problem 1ES Problem 2ES: Suppose that a function fx,y is differentiable at the point 1,2 with fx1,2=1andfy1,2=3.Iff1,2=2,... Problem 3ES Problem 4ES Problem 5ES: Use Definitions 13.4.1 and 13.4.2 to prove that a constant function of two or three variables is... Problem 6ES: Use Definitions 13.4.1 and 13.4.2 to prove that a linear function of two or three variables is... Problem 7ES: Use Definition 13.4.2 to prove that fx,y,z=x2+y2+z2 is differentiable at 0,0,0 . Problem 8ES: Use Definition 13.4.2 to determine all values of r such that fx,y,z=x2+y2+z2r is differentiable at... Problem 9ES: Compute the differential dzordw of the function. z=7x2y Problem 10ES: Compute the differential dzordw of the function. z=exy Problem 11ES: Compute the differential dzordw of the function. z=x3y2 Problem 12ES: Compute the differential dzordw of the function. z=5x2y52x+4y+7 Problem 13ES: Compute the differential dzordw of the function. z=tan1xy Problem 14ES: Compute the differential dzordw of the function. z=e3xcos6y Problem 15ES: Compute the differential dzordw of the function. w=8x3y+4z Problem 16ES: Compute the differential dzordw of the function. w=exyz Problem 17ES: Compute the differential dzordw of the function. w=x3y2z Problem 18ES: Compute the differential dzordw of the function. w=4x2y3z73xy+z+5 Problem 19ES: Compute the differential dzordw of the function. w=tan1xyz Problem 20ES: Compute the differential dzordw of the function. w=x+y+z Problem 21ES: Use a total differential to approximate the change in the values off from P to Q. Compare your... Problem 22ES: Use a total differential to approximate the change in the values off from P to Q. Compare your... Problem 23ES: Use a total differential to approximate the change in the values off from P to Q. Compare your... Problem 24ES: Use a total differential to approximate the change in the values off from P to Q. Compare your... Problem 25ES: Use a total differential to approximate the change in the values off from P to Q. Compare your... Problem 26ES: Use a total differential to approximate the change in the values off from P to Q. Compare your... Problem 27ES: Determine whether the statement is true or false. Explain your answer. By definition, a function... Problem 28ES: Determine whether the statement is true or false. Explain your answer. For any point x0,y0 in the... Problem 29ES: Determine whether the statement is true or false. Explain your answer. If fxandfy are both... Problem 30ES: Determine whether the statement is true or false. Explain your answer. The graph of a local linear... Problem 31ES: In the accompanying figure a rectangle with initial length x0 and initial width y0 has been... Problem 32ES: The volume V of a right circular cone of radius r and height h is given by V=13r2h. Suppose that the... Problem 33ES: (a) Find the local linear approximation L to the specified function f at the designated point P. (b)... Problem 34ES: (a) Find the local linear approximation L to the specified function f at the designated point P. (b)... Problem 35ES: (a) Find the local linear approximation L to the specified function f at the designated point P. (b)... Problem 36ES: (a) Find the local linear approximation L to the specified function f at the designated point P. (b)... Problem 37ES: (a) Find the local linear approximation L to the specified function f at the designated point P. (b)... Problem 38ES: (a) Find the local linear approximation L to the specified function f at the designated point P. (b)... Problem 39ES: (a) Find the local linear approximation L to the specified function f at the designated point P. (b)... Problem 40ES: (a) Find the local linear approximation L to the specified function f at the designated point P. (b)... Problem 41ES: In each part, confirm that the stated formula is the local linear approximation at 0,0.... Problem 42ES: Show that the local linear approximation of the function fx,y=xyat1,1isxy1+x1+y1 Problem 43ES: In each part, confirm that the stated formula is the local linear approximation at 1,1,1.... Problem 44ES: Based on Exercise 42, what would you conjecture is the local linear approximation to xyzat1,1,1?... Problem 45ES: Suppose that a function fx,y differentiable at the point 1,1 with fx1,1=2andf1,1=3.LetLx,y denote... Problem 46ES: Suppose that a function fx,y is differentiable at the point 0,1 with fy0,1=2andf0,1=3.LetLx,y denote... Problem 47ES: Suppose that a function fx,y,z is differentiable at the point 3,2,1andLx,y,z=xy+2z2 is the local... Problem 48ES: Suppose that a function fx,y,z is differentiable at the point 0,1,2andLx,y,z=x+2y+3z+4 is the local... Problem 49ES: A function f is given along with a local linear approximation L to f at a point P. Use the... Problem 50ES: A function f is given along with a local linear approximation L to f at a point P. Use the... Problem 51ES Problem 52ES Problem 53ES: The length and width of a rectangle are measured with errors of at most 3 and 5, respectively. Use... Problem 54ES: The radius and height of a right circular cone are measured with errors of at most 1 and 4,... Problem 55ES: The period T of a simple pendulum with small oscillations is calculated from the formula T=2L/g,... Problem 56ES: The speed of sound in a medium of bulk modulus B and density is =B Use a differential to estimate... Problem 57ES: The magnitude E of an electric field at a point outside a charged spherical shell is proportional to... Problem 58ES: According to the ideal gas law, the pressure, temperature, and volume of a confined gas are related... Problem 59ES: Suppose that certain measured quantities x and y have errors of at most rands, respectively. For... Problem 60ES: The total resistance R of three resistances R1,R2,andR3, connected in parallel, is given by... Problem 61ES: The area of a triangle is to be computed from the formula A=12absin, where a and b are the lengths... Problem 62ES: The length, width, and height of a rectangular box are measured with errors of at most r (where r is... Problem 63ES: Use Theorem 13.4.4 to prove that fx,y=x2siny is differentiable everywhere. Problem 64ES: Use Theorem 13.4.4 to prove that fx,y,z=xysinz is differentiable everywhere. Problem 65ES Problem 66ES Problem 67ES: Discuss the similarities and differences between the definition of "differentiability" for a... format_list_bulleted
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