1. Find the equation of the normal line at a given point. y = - @ (5,1)

Q: 5. Find the area of the region bounded by the xr-axis and the graph of f(x)= -over the interval (-o.…

A:

Q: Find div F and curl F if F(x, y, z) = x’i – 7j + yzk. - div F= curl F=

A: Given that     F(x,y,z) = x5i - 7j + yzk

Q: Evaluate the upper and lower sums fo n = 2, 4, 8. Illustrate with diagrams. %3D

A: answer is in next step

Q: Evaluate the line integral -ydx + dy along the curve C: y = 30x from (30, 30) to (0,0). %3D NOTE:…

A:

Q: 3x? (x³ + 4)* dæ = 5120 Select one: O True O False

A:

Q: Find the exact area under the curve between the indicated values of x. 3 ; between x = 1 and x = 3

A:

Q: The particular solution that satisfies the differential equation and the initial condition of dy/dx…

A:

Q: si 2V ædx = 104/3 Select one: O True O False

A:

Q: x = x1 + x2 x2 = -2x1 + 4x2 х1 (0) %3D 1; х-(0) 3D 0 %3D

A:

Q: 1. Find the equation of the normal line at a given point. 5 y = - @ (5,1) ||

A:

Q: Write an equation for the ellipse that has vertices (+7,0) and co-vertices (0, +6). Provide your…

A: Vertices : (7,0) and (-7,0)Co-Vertices: (0,6) and (0,-6)Vertices are of the form : (h±a , k)h+a=7 ,…

Q: a) fr'(2+x*)'dx bf sin(nx) dx )fx* In xdx

A: According to guidelines  we must answer only three of multipart questions. Please resubmit the…

Q: One of the correct steps to evaluate x2Inx dx to yield the correct integral

A: Our Aim is to identify the correct step to evaluate ∫x2 ln (x) dx to yieldthe correct integral.

Q: A candy box is made from a piece of cardboard that measures 31 by 17 inches. Squares of equal size…

A: let the cut out square side be "x"length of cardboard is 31 inBreadth of cardboard is 17 inAfter…

Q: Find T(t) and N(t) at the given point. r(t) = 8 cos(t)i + 8 sin(t)j; t= 3 T() N(G) .3

A: To find the vectors T(t) and N(t)  for the given r(t) at point t=pi/3.

Q: For the given vectors a and b, find the cross product a x b. = (4, 0, –3), b = (2, 3, 0) a x b =

A:

Q: y" + y' – 2y = 2t, y(0) = 0, y'(0) = 1

A:

Q: Given that a parallelogram is officially defined as a "quadrilateral with opposite sides that are…

A: We need to prove the property.

Q: Find the area of the plane region bounded by y = x3, x = -2 and x = 2.

A:

Q: Adjust the domain of the rectangular equation, if necessary. y = x^2-7

A:

Q: S- x+dx Using trigonometric substitution, (1+x?) tan4ode A sece В None tan+Od0 sec20 sin4ode (D coso…

A:

Q: у" - у'— бу %3D 2, у (0) %3D 0, y'(0) = 0

A: Given that     y" - y' -6y = 2 , y(0)=0 , y'(0) = 0

Q: A tank contains 3 kg of salt dissolved in 430 L of water. A salt solution of 0.01 kg salt/L is…

A:

Q: Solve the following initial valued problem x²y' + 2xy = e*, y(1) = 0

A: To find the solution of the given initial value problem.

Q: For the following demand function, find (a) E, and (b) values of q (if any) at which total revenue…

A:

Q: Convert x = 6 to an equation in polar coordinates in terms of r and 0. (Use symbolic notation and…

A: Given: x=6

Q: A cylindrical can is being filled at the rate of at =3t" , h(t) describes the height of the…

A:

Q: Find the area of the region bounded by y = (1/8)(-x² + 6x + 7) and y = -6. Answer: Find the area of…

A:

Q: Use the indicated substitution to evaluate the integral. • 7/2 dx, x = 7 sin(0) V49 x2 (Give an…

A:

Q: For the given cost function C(1) = 128/a + find 512000 a) The cost at the production level 1800 b)…

A: "According to the guidelines issued by the company we are supposed to answer only first three…

Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) Y,…

A:

Q: Find the general solution of the following differential equation. y''' +y'' + 3y' −5y = 0 [Hint:…

A: Use the auxiliary equation for finding the other roots and general solution.

Q: 5n

A:

Q: y" – 2y' + y = Ita² 1+x?

A: We use the method of variation of parameters

Q: 2. Find S +l" dudy by first snitching the order of integration 4

A:

Q: You are assigned a task to design three rectangular cubicles lined up and sharing walls as in the…

A:

Q: What trigonometric substitution should be used to evaluate ? A x=3 sec® B x=3 tan0 x= 3sin0 D) None…

A:

Q: ||r'(t) × r"(t)|| ||r"(t)||* Use the formula k(t) to find k(t). r(t) = 4 cos(7t)i+4 sin(7t)j + 3tk…

A:

Q: 3 dy Зу =-sin -1 2 - sin +C V4-9y2 3 A) True B) False

A:

Q: A restaurant has an annual demand for 884 bottles of California wine. It costs $3 to store 1 bottle…

A:

Q: Determine if the following functions are odd, even, or neither. Provide reason. (a) f(x) = x² (b)…

A:

Q: x²– 9 ?

A:

Q: Find the area of the plane region bounded by y = x2 - 4x and y = x(2-x). Answer:

A:

Q: Find exactly T(t) and N(t) for x = e'cost, y = e'sint, z = e' for t = 0. [Choose the correct…

A: This question can be solved using the concept of tangent and normal in vector form.

Q: 4. Use partial fraction decomposition to evaluate dx x' + 4x +3 2

A:

Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise. O…

A:

Q: You record the temperature every hour from midnight until 8:00a.m. You see that the temperatures (in…

A:

Q: The most conveneient way to evaluate xx2-4 by substitution is to let x2- A True B) False

A: We have to find out

Q: Solve the problem. Write an iterated triple integral in the order dz dy dx for the volume of the…

A: Write an iterated triple integral in the order dz dy dx for the volume of the region in the first…

Q: Wage Gap Between Men and Women The bar graph shows the wage gap between men and women for selected…

A: To find G(10) and interpret it.