1. Find the divergence and curl of the following vector fields a. F = (1/y²)j b. F=y³z³i+ 2xyz³j + 3xy²z²k c. F=xyz²i+x²yz²j+x²y²zk

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A: The graph of the function y=1x2 is:

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A: Solution is given below:

Q: solve for exercise 11, provide full and complete procedure

A: topic:- application of integration

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A: I am attaching image so that you understand each and every step. Please take exact value then we get…

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A: This question can be solved using the concept of system of linear equations.

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A: To find out values.

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A: We have to solve ∫02e-2x2dx   by  using Taylor series            since,  we know that…

Q: 4. Given f(x) = sin² (2x) find the slope at (5, 1) a)-√3 b) √3 d) 0.1395

A: As we know that; The slope of the tangent line to the given curve is equal to the derivative of the…

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A: The solution is given below

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Q: ve the following: y' - x³y² = 4x³, y(0) 4x³, y(0) = 2.

A: We will solve the differential equation

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Q: Question 8 of 10, Step 1 of 1 Let h(x) = √√x + 5. Find the function given below. h(4n+ 9), n >…

A: Let hx=x+5To find the value of the function given below.h4n+9=?where n≥-72

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A: If 0<x-8<δ, then -4x+32<ε

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A: We can answer both the question as below.

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A: Consider the following repeating decimal. 0.5To write the repeating decimal as a geometric series.

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A: See this solution in below

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A: Aim: Dxf(g(2)) We know that,…

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A: Given function,fx, y = 5x -4y

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A: We need to fill in the blanks.

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Q: Consider the relation R defined on the set X={a,b,c,d} and Y={1,2,3,4} from X to Y, where R= {(?,…

A: Disclaimer: Since you have  asked multiple question ,we will solve first question for you . if you…

Q: 6. Find y" give y = 7³x a) 21³x In(7) b) 63³x In(3) c) 3(7³x)ln(3) d) 9(7³x)(ln7)

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A: The solution is given below

Q: (b) ſ sin³(x) -dr cos (1)

A: Let's solve given integration.

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Q: Let f(x, y, z) = 3xz + sin(ry)e*. what is faz? Find the gradient at the point (0, 0, 0)?

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…