Find div F and curl F if F(r, y, z) = 2e*"i– 9cos yj+ 4 sin² z k. div F= curl F=

Q: Find the area bounded by the curve r= 2+cos θ

A: Given problem:- Find the area bounded by the curve r= 2+cos θ

Q: A function g(x) has the following graph: 5. -2 2. What is lim g()? does not exist IN

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Q: b. S 2*³-4x²-x-3 dx х2-2х-3

A: First we divide the polynomial  using long division

Q: given poim arctan(2) f(x, y) = arctan (4, -4) f(X, y) = x, ) = (4, -4) = (4,-4) =

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

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Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

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Q: 'ind V · (V × F) if F(x, y, z) = 9 sin ci + 5 cos(9x – 10y)j + 2zk. - V · (V × F) =

A: To find div (curl F).

Q: Solve the general solution of DE: y" -5y' + 4y = 3e6r O y = cje* + c2er + ner 10 y = cje* + czet* +…

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Q: Find div F and curl F if F(x, y, z) = 14y°z°i – 10x°z°j – 5xy°k. 35: 6.8 - div F= curl F=

A: We have to find div F and curl F.

Q: function f has the following graph: 4- 3 2 1. -1 6 7. 8 -1 -2 Vhich of the following is true? O The…

A: Given query is to find the correct statement for the function.

Q: Find the partial derivative. revIlzy

A: We can find the partial derivative as below.

Q: The position vector r describes the path of an object moving in space. Find the velocity v(t), speed…

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Q: ||r'(t) × r"(t)|| ||r(t)||* Use the formula k(t) to find k(t). r(t) = e*i+e*j ,3t: K(t) =

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Q: ||r(t) × r"(t)|| ||r(t)||* Use the formula k(t) to find «(t). 13 r(t) = t'i+ t®j 30 t3 K(t) V4 + 25…

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Q: Question 3 of 4 (x² + 1)5 y = (23 – 1) – 1)

A: According to guidelines, we must answer only one question of the multiple questions given. Please…

Q: Find the radius of convergence, R, of the series. Σ n = 1 R = Find the interval, I, of convergence…

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Q: Find the curvature and the radius of curvature at the point t = 0. x = e' cos(t), y = e' sin(t), z =…

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Q: Which type of discontinuity does the function exhibit at x = 3? -x2 + 1, -1 sx <0 2х, f(x) = { -4,…

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Q: Find curl (5z i + 6x j + 8y k). curl (5z i+ 6x j + 8y k) )i + ( i )j + ( i i )k

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Q: Find the area bounded by the indicated curves. y = 3x + 3, y = x2 + 3 Optional For visualization,…

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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.

Q: A company is planning to manufacture snowboards. The fixed costs are $400 per day and total costs…

A: Cost

Q: 1. Using L'Hospital's rule, evaluate lim(1 – x²).

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Q: Find the indefinite integral. (Use c for the constant of integrat (4t3i + 4tj – 6vik) dt

A: we use the basic formula ∫xn dx =xn+1n+1+C    ; n≠-1

Q: d,x+7 3. dx 2x-3

A: To find: ddxx+72x-3

Q: Write and evaluate the definite integral that represents the volume of the solid formed by revolving…

A: We have to integrate the function to calculate volume

Q: Find T(t) and N(t) at the given point. r(t) = (t – 5)i + tj; t= 5 T(5) N(5) =

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Q: If f (x) : 2, what is the equation of the line tangent to f(x) at x = –1? O y+24x + 36 = 0 O y – 24x…

A: Given query is to find the equation of the tangent.

Q: ction f has the following graph: -1 4. of the following is an infinite limit? m f(r) +0+ f(x) m f(z)…

A: Topic:- limit calculus

Q: Describe the graph of the equation. r = (7 – 21) i+ 101j O Itis a line in 2-space through the point…

A: Equation

Q: The rate of growth dP/dt of a population of bacteria is proportional to the square root of t, where…

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Q: Find V × (V × F) if F(x, y, z) = 9xyj+10xyz k. V x (V × F) =|

A: We have to find given expression.

Q: Find div F and curl F if F(x, y, z) = x²i – 5j + yzk. 2: - div F= curl F=

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Q: Find the equation of the line tangent to the function f(x) = (x – 1)3 + 2 at x = 1. O y = 2 O y – 2…

A: Given query is to find the equation of the tangent at x = 1.

Q: Find a Taylor Series for the function about x = 0. F(x) = In(3 + 4x) %3D

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Q: y = 3x - x² and y = 2x %3D

A: See the details solution in below

Q: Find the Taylor series for f(x) centered at the given value of a. [Ass f(x) = In(x), a = 6 |(-1)*+1…

A: We can solve this as follows:

Q: Differentiate the following functions: 1) f (x) = 5 2) f (x) = -2x 3) ƒ (x) = -2x + 2 -2r +2 %D

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: A plane region is bounded by the curves 2x2 + 4x + y = 0 and 2x – y = 0. Sketch the given boundaries…

A: The objective of the question is evaluate the area bounded by the given curves and Sketch of the…

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

A: As we know that; The Green's theorem; ∫CPdx+Qdy=∫∫D∂Q∂x-∂P∂ydA   Given: I=∫C3xy dx+6xy dy And C:…

Q: Which integral corresponds to the volume of the solid generated by revolving the region enclosed by…

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Q: 5. Evaluate the indefinite integral sin2x 1+ cos?x

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Q: 3 Let F(t) = < 3 2t 3t -1' 3 - 5' 4 -3 Find F (t) F'(t) - < Question Help: D Video Add Work

A: Given: Now, we need to find r→'(t). r→'(t)=33t-1' , 2t3t2-5', 2t24t3-3'        =-93t-12,…

Q: Obtain the limits of the following functions: (2sinx-sin2x 1. lim x-sinx

A: To evaluate the limit of the function.

Q: (a) If f(x)dx = 11 and F(9) = 17, find F(5). F(5) eTextbook and Media 300 (b) If f(x)dx = 0, what is…

A: We have to find the value and the relationship.

Q: ||r(t) × r"(t)|| Use the formula k(t) to find k(t). r(t) = t'i+ t°j K(t)

A: The given formula is; κt=r't×r''tr't3 And rt=t2i+t9j

Q: The integral tan x sec?x dx is an improper integral of type I that diverges none of them is an…

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Q: Determine whether the series converges or diverges. Make sure to clearly state the test that you're…

A: Given,  ∑n=0∞2xnn!

Q: Given the function f(x) = x² and the closed interval [0, 1], which of the following is a value of c…

A: Given query is to find the value of c.

Q: Find V · (V x F), if F(x, y, z) = 5e*?i+ 9xe"j – 6e²k. V · (V × F) =

A: