Locate the stationary points of the function. f(x) = (z-1)² +6 f'(x) = Find when f'(x) = 0, hence find: x-coordinate of the stationary point giving a minimum = x-coordinate of the stationary point giving a maximum = X

Q: Evaluate the line integral, where C is the given curve. (z² + 2xy)dx + x²dy + 2xzdz, where C is the…

A:

Q: Evaluate the definite integrals using properties of the definite integral and the fact that 3 3…

A: To evaluate the following integrals by using the properties of the definite integral and the fact…

Q: 13. The supply function for a certain product is p = S(x)=x²+2x+32 where p is the price in dollars…

A:

Q: Let z(x, y) = xey where x = t³ & y = 3₁+ 4t. dx dy dz dt dt dt Calculate dx dt = by first finding =…

A:

Q: Find [x²³zds x²z ds, where C is the line segment from (0,4,-4) to (-5,1,-10)

A: Find ∫Cx2zds, where C is the line segment from(0,4,−4) to (−5,1,−10)

Q: Select the equation of the parabola with vertex (3, 2) and directrix y=-1. O(x-3)² =12(y-2) ○ (x-3)²…

A:

Q: Find the value of the Riemann sum Σk-1 f(ck) Vk for the function f(x) = x² + 2 using the partition…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 3 If f(x) is an even function, and if ſ³ 6ƒ(x)dx S³3 f(x) dx. = 15, find

A:

Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = ln(2x + 3y +6z). F(x, y, z) = 2 Check…

A:

Q: When a model rocket is launched, the fuel burns for a few seconds, accelerating the rocket upward.…

A: We have to find the velocity and time from the given graph.First we will conclude information from…

Q: A particle's velocity is given by the expression v(t) = 3 + 4t + 3t ¾ m/s. a) write the expression…

A:

Q: Consider the partial graph of a transformed sinusoidal curve with a domain of z ER. 5.3. 5: 4 3 2 F…

A: If  is an invertible function, then its inverse is given by .

Q: Fill in the blanks for both missing numerators and denominators to set up partial fraction…

A: The given rational expression .The aim is to setup the partial fraction decomposition for the…

Q: Evaluate the surface integral below where S is the cone with given parametric equations (x² + y² −…

A:

Q: 22. A sphere is put inside a sealed right cone so that the highest point of the sphere touches the…

A:

Q: Find a Taylor polynomial of 3rd degree centered at a=1 for the fuction f(x) = = 01- (x-1) + 2(x -…

A: Solution- The formula of Taylor polynomial is,here n=3 ( because we are calculating for 3rd the…

Q: You would like to purchase a Tesla Model 3 car for $55000. The average rate of depreciation of the…

A:

Q: The function shown on the graph above, has the formula f(x) Prove algebraically or numerically that…

A:

Q: Find the absolute maximum and minimum values of the following function on the given interval. Then…

A:

Q: The force exerted by an electric charge at the origin on a charged particle at the point (x, y, z)…

A:

Q: Identify the coordinates of any local and absolute extreme points and inflection points. Graph the…

A:

Q: (a) Determine the profit function. Include units! P(x) = = (b) Determine the marginal profit when x…

A:

Q: Given the following relation between x and y answer the following question. Using implicit…

A:

Q: At time, t, in seconds, your velocity, v, in meters/second is given by the following. v(t) = 8 + 7t²…

A:

Q: Find the coordinates of the stationary points of the function. f(x) = 2x³ + -1x² - 60x +9 f'(x) = f"…

A:

Q: Evaluate 28 - 19 the definite integral d x

A: Evaluate the definite integralI=∫−1928dx

Q: Please detailed and dont do handwritten. provided x is not equal to 0, a geometric progression with…

A:

Q: Find cos (x² + y²)dA where D = {(x, y) | 9 ≤ x² + y² ≤ 36 Round your answer to four decimal places.

A:

Q: Use the chain rule to find əz Ər =√r-2,0=π/6 if z = xye*/, x=rcos 0, y = rsin 0:

A:

Q: The following relationship is know to be true for two angles A and B:₁ sin(A) cos(B) + cos(A) sin(B)…

A: Formula of sin( A + B ) is given as follows

Q: 3 √ √ ² (6 + Evaluate the integral 2 dr.

A:

Q: Find the indicated partial derivatives of f(x, y) = 3x³y² using the limit definition. The limits…

A:

Q: (b) (-1,√3) (1) Find polar coordinates (r, 0) of the point, where r> 0 and 0 ≤ 0 < 2π. (C (r, 0) =…

A:

Q: Use a triple integral to find the volume of the solid enclosed between the cylinder x² + y² = 9 and…

A:

Q: Suppose F(3) = 5, F(4)— —13, and F'(x) = f(x). suppose G(3) = —13, G(4) = 10, and G'(x) = g(x). (8…

A: Suppose F(3)=5,F(4)=−13, and F′(x)=f(x).  Also suppose G(3)=−13,G(4)=10, and G′(x)=g(x).

Q: Y = x (x+4)

A: Logarithmic differentiation is done by first taking logarithm on both sides of the equation and then…

Q: Consider the vector field on R2. The associated one-form is: 3 || F(x, y) = (xy + 5x + y, x³y¹4)

A: .To write the associated one-form.

Q: Connecting the Start Capacitor The spacecraft is nearly ready for takeoff! The last task is to…

A:

Q: Given the graph f(x), find f f(x) dx using formula(s) from geometry. Enter an integer or a fraction.…

A:

Q: 3 √ √ ² (6 + Evaluate the integral 2 dr.

A:

Q: 1 2 n(Inn)2 (f) Σ

A:

Q: set up and evaluate an integral for the volume of the solid in the first octant and bounded by the…

A:

Q: Find the volume of the solid that is bounded above by the cylinder z = x² and below by the region…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Determine whether the line _x=3+8t, y=4+5t, z= −3−t is parallel to the plane x-3y + 5z = 12.

A: The line  and the plane  are parallel if

Q: Differentiability of f(x,y) at point (a,b) Let f: R²R be a function given by f(x,y) ry if (x,y)…

A: Let  be a function given byTo show: whether  is differentiable at point .

Q: 12 A population of yeast cells devleops with constant relative growth rate of 0.4159 per hour. The…

A: A population of yeast cells develops with constant relative growth rate of  per hour.The initial…

Q: Let f(x, y) = x² + 2y + 40xy. List the critical points:

A: Solution-

Q: 1 Find the local and absolute extreme values of the function f(x)=x√1-z on [-1,1] (Show your work)

A: Absolute extrema are the largest and smallest value of a function that will ever be.

Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = ln(x + 6y + 2. F(x, y, z) =

A:

Q: (d) Σ 2 η-1 Vn2 – 1(n + 1)

A: