This Question: 3 pts 4 of 35 This Test: 100 pts possible dy If F(x,y) 0 and y is a differentiable function of x, explain how to find dx Choose the correct answer below. O A. Use the chain rule when taking the derivative of the left side of the equation with respect to dy and setting it equal to dx O B. Use the chain rule when taking the derivative of both sides of the equation with respect to x and then solve for dy dx O C dv Use the chain rule when taking the derivative of both sides of the equation with respect to y and then solve for dx O D. Use the partial derivatives to determine dy 히증 히증
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Explain how to compute the surface integral of scalar-valued function f over a sphere using an explicit description of...
Question 14 7 pts Consider the line integral F. dr where REC IND РІ. F(x, y,...
Question 14 7 pts Consider the line integral F. dr where REC IND РІ. F(x, y, z) = i + (x+yz)j + (xy – z)k and C is the boundary of the plane 2 + y + z = 4 in the first octant, oriented in the counterclockwise direction when viewed from above. the following double integrals is equivalent to this line Using Stokes' Theorem, which integral? °6964 (3 - 2z+1) du dz (2x + y) dy da Question 12...
The given point is on the curve. Find the lines that are (a) tangent and (b)...
The given point is on the curve. Find the lines that are (a) tangent and (b) normal to the curve at the given point. 4x2 + 3xy + 3y2 +17y - 4 = 0,(-1,0) (a) Give the equation of the line that is tangent to the curve at the given point y = (b) Give the equation of the line that is normal to the curve at the given point. y = Suppose that fis an odd function of x....
Question 6 6 pts Suppose that f(x, y, z) is a scalar-valued function and F(x, y,...
Question 6 6 pts Suppose that f(x, y, z) is a scalar-valued function and F(x, y, z) = (P(x, y, z), Q(2,y,z), R(x, y, z)) is a vector field. If P, Q, R, and f all have continuous partial derivatives, then which of the following equations is invalid? O curl (aF) N21 = a curl F for any positive integer Q. REC o div (fF) = fdiv F+FVF Odiv curl F = 0 O grad div f = div grad...
problem 34 Equations with the Independent Variable Missing. If a second order differential equation has the...
problem 34
Equations with the Independent Variable Missing. If a second order differential equation has the form y"f(y, y), then the independent variable t does not appear explicitly, but only through the dependent variable y. If we let y', then we obtain dv/dt-f(y, v). Since the right side of this equation depends on y and v, rather than on and v, this equation is not of the form of the first order equations discussed in Chapter 2. However, if we...
Evaluate the integral Vs««, », z) ds over the surface o represented by the vector-valued function...
Evaluate the integral Vs««, », z) ds over the surface o represented by the vector-valued function " (u, v). sus2,05vs f(x, y, z) = 3xyz; r(u, v) = u cos vi+ u sin vj +4u k (1 sus 2 Enter the exact answer. 15x,y,z) as = ? Edit
Evaluate the integral Ms (x, y, z) ds over the surface o represented by the vector-valued...
Evaluate the integral Ms (x, y, z) ds over the surface o represented by the vector-valued function r (u, v). -; r(u, v) = 7 u cos vi+7 u sin vj + 7 u’ k (0 sus sin v, 0 SV ST) 9 f (x, y, z) = 49 + 4x2 + 4y2 Enter the exact answer. 144 f (x, y, z) dS = ? Edit 0 action Attornten of 1
3x+2 f(x) =( :) (x-> +1) Your problem: using the rules of differentiation, find the derivatives...
3x+2 f(x) =( :) (x-> +1) Your problem: using the rules of differentiation, find the derivatives of the collowing: f)-(3442) fool(3x+2) (-5x + x + 1) - 2 1 =(-15x 10x" + (-2x = 2) =>15x410x5 - 2x = = 3x -3x- 27 (X)(3+0)-(3x+2)(1) x² g'=(x) =F12x15x4_2 = -5x6 xb * please check my work, if wrong, please write out correct solation! Chain Rule: When functions are composed, to take the derivative involves both the outside function and the inside...
Find an equation of the tangent plane to the surface at the given point. x2 +...
Find an equation of the tangent plane to the surface at the given point. x2 + 2z2ev - * = 22, P= (2, 3, te) Use the Chain Rule to calculate f(x, y) = x - 4xy, r(t) = (cos(5t), sin(3t)), t = 0 force) = +-/1 points RogaCalcET3 14.5.015. Use the Chain Rule to calculate f(x, y) = 5x - 3xy, r(t) = (t?, t2 - 5t), t = 5 merce) = + -/1 points RogaCalcET3 14.5.018. Use the...
Problem 1. (a) The radius of a sphere is increasing at a rate of 4 mm/s....
Problem 1. (a) The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing when the diameter is 80 mm? dy dx (b) If x+y+z-9, dt 5, and -4, find dt dz dt when (x, y, z)-(2,2,1). Problem 2. (a) Find the derivative of the function yr e-****** (b) Find the derivative of the function y - In(x* +100). cos. Problem 3. Use logarithmic differentiation to find the derivative of the function...
U Question 15 "C 7 pts "С If S is the surface of the cylinder E=...
U Question 15 "C 7 pts "С If S is the surface of the cylinder E= {(x,y,z) : 32 + y < 4,1523}, oriented outwards, which of the following (after applying the Divergence Theorem) will compute zyz) - dS? 40 O (1 + y2 cos & sin 6)r dr de dz REC O 1988 6%" /*(1 + == sin ®)r dr do dz %%% %%% %%% (r cos 0 + 32 + y2 z cos ( sin 0), dr do...
Question 14 7 pts Consider the line integral F. dr where REC IND РІ. F(x, y, z) = i + (x+yz)j + (xy – z)k and C is the boundary of the plane 2 + y + z = 4 in the first octant, oriented in the counterclockwise direction when viewed from above. the following double integrals is equivalent to this line Using Stokes' Theorem, which integral? °6964 (3 - 2z+1) du dz (2x + y) dy da Question 12...
The given point is on the curve. Find the lines that are (a) tangent and (b) normal to the curve at the given point. 4x2 + 3xy + 3y2 +17y - 4 = 0,(-1,0) (a) Give the equation of the line that is tangent to the curve at the given point y = (b) Give the equation of the line that is normal to the curve at the given point. y = Suppose that fis an odd function of x....
Question 6 6 pts Suppose that f(x, y, z) is a scalar-valued function and F(x, y, z) = (P(x, y, z), Q(2,y,z), R(x, y, z)) is a vector field. If P, Q, R, and f all have continuous partial derivatives, then which of the following equations is invalid? O curl (aF) N21 = a curl F for any positive integer Q. REC o div (fF) = fdiv F+FVF Odiv curl F = 0 O grad div f = div grad...
problem 34
Equations with the Independent Variable Missing. If a second order differential equation has the form y"f(y, y), then the independent variable t does not appear explicitly, but only through the dependent variable y. If we let y', then we obtain dv/dt-f(y, v). Since the right side of this equation depends on y and v, rather than on and v, this equation is not of the form of the first order equations discussed in Chapter 2. However, if we...
Evaluate the integral Vs««, », z) ds over the surface o represented by the vector-valued function " (u, v). sus2,05vs f(x, y, z) = 3xyz; r(u, v) = u cos vi+ u sin vj +4u k (1 sus 2 Enter the exact answer. 15x,y,z) as = ? Edit
Evaluate the integral Ms (x, y, z) ds over the surface o represented by the vector-valued function r (u, v). -; r(u, v) = 7 u cos vi+7 u sin vj + 7 u’ k (0 sus sin v, 0 SV ST) 9 f (x, y, z) = 49 + 4x2 + 4y2 Enter the exact answer. 144 f (x, y, z) dS = ? Edit 0 action Attornten of 1
3x+2 f(x) =( :) (x-> +1) Your problem: using the rules of differentiation, find the derivatives of the collowing: f)-(3442) fool(3x+2) (-5x + x + 1) - 2 1 =(-15x 10x" + (-2x = 2) =>15x410x5 - 2x = = 3x -3x- 27 (X)(3+0)-(3x+2)(1) x² g'=(x) =F12x15x4_2 = -5x6 xb * please check my work, if wrong, please write out correct solation! Chain Rule: When functions are composed, to take the derivative involves both the outside function and the inside...
Find an equation of the tangent plane to the surface at the given point. x2 + 2z2ev - * = 22, P= (2, 3, te) Use the Chain Rule to calculate f(x, y) = x - 4xy, r(t) = (cos(5t), sin(3t)), t = 0 force) = +-/1 points RogaCalcET3 14.5.015. Use the Chain Rule to calculate f(x, y) = 5x - 3xy, r(t) = (t?, t2 - 5t), t = 5 merce) = + -/1 points RogaCalcET3 14.5.018. Use the...
Problem 1. (a) The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing when the diameter is 80 mm? dy dx (b) If x+y+z-9, dt 5, and -4, find dt dz dt when (x, y, z)-(2,2,1). Problem 2. (a) Find the derivative of the function yr e-****** (b) Find the derivative of the function y - In(x* +100). cos. Problem 3. Use logarithmic differentiation to find the derivative of the function...
U Question 15 "C 7 pts "С If S is the surface of the cylinder E= {(x,y,z) : 32 + y < 4,1523}, oriented outwards, which of the following (after applying the Divergence Theorem) will compute zyz) - dS? 40 O (1 + y2 cos & sin 6)r dr de dz REC O 1988 6%" /*(1 + == sin ®)r dr do dz %%% %%% %%% (r cos 0 + 32 + y2 z cos ( sin 0), dr do...
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