дz Find the value at point (1,1,1) if the equation: дх xy + z3x – 2xy...
дz дz 1. In the equation, x sin y - y cos z + xyz = 0, z is a function of x and y. Find and ду" дх D- 1) and o- (-11 1)
Find the first partial derivatives of the function z = (3х + 8y)1. дz 1. ІІ дх дz. 2 . ІІ ду
Observe that the point (1,1,1) satisfies the equation 2. Although we may not be able to write down a formula for z in terms of x and y there is a function z(x,y) that has continuous partial derivatives, is defined for (x,y) near (1,1), and for which z(1,1) 1. For this function find the values of the partials дг/дх (1,1) and дг/ду (1,1). Use this to approximate z(1.1 ,9). Finally, find Эгјах (1,1). If we try to do similar calculations...
Observe that the point (1,1,1) satisfies the equation 2. Although we may not be able to write down a formula for z in terms of x and y there is a function z(x,y) that has continuous partial derivatives, is defined for (x,y) near (1,1), and for which z(1,1)-1. For this function find the values of the partials дг/дх (1,1) and дг/ду (1,1). Use this to approximate z(1.1 ,.9). Finally, find az/0x (1,1). If we try to do similar calculations for...
In R”, find a point normal equation for the plane II which contains the line (1,1,1) + t(15, -6, -2) together with the point Q(–7, 18, –2) Answer: one such point normal equation for II is X +
Q3. Find the value of az/ax at the point (1, 1, 1) if the equation xy + z’x – 2yz = 0 defines z as a function of the two independent variables x and y and the partial derivative exists. (2 marks)
Question 4 Solve the differential equation. 2xy' + y = 2V* Question 5 Solve the initial value problem xy' + y = xln x , y(1) = 0 Question 7 Find the derivative. c = tet, g =t+ sin t Question 8 Find the equation of the tangent to the curve at the given point. x = ť – t, y=ť +t+1 ; (0,3)
Find an equation of the plane tangent to the following surface at the given point. xy +6yz +xz- 32-0, (2.2,2) The equation of the tangent plane at (2.2.2) is-0
Use to fundamental theorem of line integrals to evaluate F dr for 6. F(xy) = (2xy,x2 -y) over the path C from the point (2, 0) to (0, 2) Use to fundamental theorem of line integrals to evaluate F dr for 6. F(xy) = (2xy,x2 -y) over the path C from the point (2, 0) to (0, 2)
Find a recurrence relation for the power series solutions of differential equation y" - 2xy' + 8y = 0 about the ordinary point x = 0.