Find div F if F(x, y, z) = (x² + y) i + z² j + (ey - z) k. 2x - 1 O 2xy i +k O 2x i -k 2хy - 1

Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0<ts 1. (y – x) dx +…

A: Just I have used the given parametric representation of the curve C to change the given line…

Q: Consider the following. f(x) = x(x² – 11x + 35) x2 g(x) %D (a) Use a graphing utility to graph the…

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Q: d Calculate ri(t) · r2(t)] and ri(t) × r2(t)] first by differentiating d dt dt the product directly…

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Q: Use the limit definition to find the derivative of f (x), this means no short cut rules, f(x) = x? –…

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Q: k S = (d – 2)? where c and k are positive constants which depend on the quantity of smoke each stack…

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Q: Evaluate the line integral (2x + 4y)dx + (3x – 9y)dy along the curve C : æ = 2 cos t, y = 4 sin t (0…

A: We need to evaluate integral.

Q: Evaluate Sae 2a (a2 + 9) d. 3c

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Q: Use the formula K(t) = r(t) × r"(t)|| ||r(t)||* to find k(t). r(t) = 11 cos(t)i+11 sin(t)j + 6tk…

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Q: 2. Find an equation of the plane containing the point P (0, -) and the line determined by the two…

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Q: Find an equation of the plane with the given characteristics. The plane passes through the point (2,…

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Q: Which among the choices is NOT true about the continuity of f(x)? if x 1 X, メ, 2 f(x) = (2 – x), O…

A: Solution

Q: A potter forms a piece of clay into a cylinder. As he rolls it, the length, L, of the cylinder…

A: Here, the amount of the clay is fixed. dVdt=0...(1) Now, the volume of the cylinder is given by:…

Q: 0.09 ) 12t At the end of t years, the future value of an investment of $37,500 in an account that…

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Q: Evaluate the improper iterated integral. 1+ xp Áp- Submit Answer

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Q: 55. At 9 A.M., ship B is 65 miles due east of another ship A. Ship B is then sailing due west at 10…

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Q: dz and ду dz Find z = a° In (1+ cy) az dz ду ||

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Q: d d ri(t) - r2(t)] and nt) x ra(t) first by differem [ri(t) × r2(t)] first by differen dt dt the…

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Q: V(PQ),V (PR), and V(PS) are 1. Find the volume of the parallelepiped PQRS if the vectors…

A: Solution of 1st question.

Q: d Calculate ri(t) · r2(t)] and rı(t) × r2(t)] first by differentiating d dt the product directly and…

A: Given

Q: 5 4 3 1 T1/2 3π/2 -1 -2 -3 + -4 -5 The graph of the function f(x) = cot x is given above for the…

A: Solution is given below:

Q: Find the four second partial derivatives. Observe that the second mixed partials are equal. z =…

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Q: the tunchon: a certain check point is given by 30) 13 VE Find the, çar pesihon, St), af Assame that…

A: In this velocity function is given, so to find the position function we need to integrate the…

Q: 2. Show that if x and y are two vectors, then

A: Replace x→ by u→ &amp; y→ by v→     Graphing software do not accept label x, y To show: u - v ≤u±v≤u…

Q: x2 - 6x + 8 lim X 2 X - 2 1

A: The objective of the question is evaluate the limit.

Q: In chapter 10, we will be solving system of equations. Most of the time, we solve system of linear…

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Q: By using variation of parameters, what is a possible value for u'1 for the differential equation y''…

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Q: Evaluate the iterated integral. /4 y cos(x) dy dx 地

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Q: Fod ble Jecond deriyalive of Hhe Aullowing funchon g lx) = Inca=43)

A: g(x)=ln(x2+3)

Q: Laplace transform of (t+2)^2

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Q: Find the integral of your answer in problems 2a and 2b. Note: My answer on 2a and 2b will be found…

A: Here we have to find the area.

Q: Find the first partial derivatives with respect to x,y and z f/x.y.2)= 3x'y- 9xyz 1 10 yz? 9xyz + 10…

A: Given:         fx,y,z=3x2y-9xyz+10yz2 First partial derivatives with respect to x,y,z.…

Q: II. Use the first fundamental theorem of calculus to find F'(x) .Write your final answer on the box.…

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Q: 4) Find the critical points of the parametric equations x = t* – 1 y = t3 -t

A: Topic:- application of derivatives

Q: Find the area of the region enclosed by the parabolas y=x and y=2x-x². Make a sketch and shade in…

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Q: Find V x (V x F) if F(x, y, z) = 2xy j+ 6xyz k. %3D V × (V × F) =

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Q: Find div F and curl F if F(x, y, z) = x²i – 7j + yzk. div F= curl F=

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Q: A light on the ground 100 feet from a building is shining at a 6-foot tall man walking away from the…

A: A light on the ground 100 feet from a building is shining at a 6-foot tall man walking away from the…

Q: Now, let's discuss the difference cases of solution to a given system of linear equations. There are…

A: Given problem :- Now, let's discuss the difference cases of solution to a given system of linear…

Q: The outside diameter of a thin spherical shell is 12 feet. If the shell is 0.3 inch thick, use…

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Q: Using the laplace transformation formula, ∫ f(t) e^−st dt evaluate L[8t^2 e^-2t]

A: Laplace transform of the function f(x)Lf(t)=∫0∞e-stf(t)dt

Q: Solve the initial value problem y′′−10y′+50y=0 for y(0)=1 and y′(0)=5. After getting the equation…

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Q: At 10:17 a.m., you pass a police car at 55mph that is stopped on the freeway. You pass a second…

A: Here, note that the distance between two police cars is 39 miles and the time between them is…

Q: Activity 1.5.2. A potato is placed in an oven, and the potato's temperature F (in de- grees…

A: Solution: Given data

Q: Given the function g(x) 6x + 63x² + 216x, find the first derivative, g'(x). = (x),6 Notice that…

A: We use second derivative test to determine the local Maxima and minima

Q: Determine the vector field of F Flr, y) = yl – x)

A: Solution is given below:

Q: e. Suppose someone claims that C'(5000) = -0.1. What would the practical mean- ing of this…

A: We have to find the meaning of C'(2000).

Q: Verify Green's Theorem by evaluating both integrals Lr dx + x* dy = / dA ду x² dy ax for the given…

A: In this question we verify Green's Theorem                 i.e, verify integral  ∫C y2 dx +x2 dy =…

Q: A stone is thrown vertically upwards, from the edge of a 5 m tall cliff with an initial velocity of…

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Q: Evaluate the improper iterated integral. 9. x2 dy dx 1 + y?

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Q: Find the curvature and the radius of curvature at the stated point. r(t) = 5 cos(t)i+11 sin(t)j+4tk;…

A: Given problem:- Find the curvature and the radius of curvature at the stated point.   r(t) = 5cos…