If z = (x + y)e", x = 3t, y = 3-t², find dz/dt using the chain rule. Assume the variables are restricted to domains on which the functions are defined.

Q: Graph the line with the given point and slope.

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Q: Find a power series representation for the function. 8 + Χ (1 − x)2 f(x) Σ( 1) η Determine the…

A: The given function is: f(x)=8+x(1-x)2

Q: Find the domain of the function using interval notation. f(x) = -2x (x-2)(x-7) To enter oo, type…

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Q: b) Ln=1 Inn n2

A: Given query is to find series converges or diverges.

Q: 21-22 Find y' and y". 21. y = x² ln(2x)

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Q: Sin 0=4/5 Find a g 1/5 where 40 < x 180

A: sinθ=45⇒θ=arcsin45+2πn, θ=π-arcsin45+2πn⇒θ=53.13∘ +360∘ n, θ=126.87∘ +360∘ n

Q: Let f(x,y) = 2x^2 + xy −y^2. Prove that the directional derivative of f(x,y) at point x = (3,−2) in…

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Q: Find the absolute maximum and absolute minimum of the function x3 3 f(x) = 1 7x² 2 + 10x - 2 over…

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Q: Find the average value of the function y = 35 - 2x on the interval [0, 4]. O 31 10 O 20 O None of…

A: The Answers are given below

Q: (c) Find the value of √a²- [₁ 2(x+y) x² + y² giving your answer in terms of a. 1+ dx dy,

A: The given integral is  ∫0a2-x2∫-aa 1+2(x+y)x2+y2dx dy

Q: 7 п 6 S y 4 3 2 4 ·10 Average rate of change = Number 6 Estimate the average rate of change from z =…

A: To find the average rate of change of function

Q: TT X S cos dx 2 0

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Q: • [ε (a) Evaluate S (b) Evaluate 3.re dr. r² sin z dr.

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Q: Evaluate the following integrals: a. I sec¹()tan³(-)dx

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Q: 3₂ If t=15157, evalvate if possible Part 1. Sin t 13 له b) none - 이글 e) 9 + ا (a C) - 0) ) 6)-1 یہ -…

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Q: BC cuts the x-axis at D. E is a point on AC such that BA // DE. Given points A(-4,8), B(5,2),…

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Q: Question 5 Find the area bounded by the given curves. y = 0.5x 2, y = -x ² +6

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Q: Use a double integral to find the area of the region bounded by all leaves of the rose r = 5 sin 50.…

A: The given curve is: r=5 sin5θ

Q: Question Three (a) Prove that F(x, y, z)= (y² cosa+z³)i+(2y sin a-4)j+(3rz+2)k is a conservative…

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Q: The figure above shows the graph of the continuous function f. The regions A, B, C, D, and E have…

A: The area of region A =5It is above x - axis therefore, ∫-7-5f(t)dt = 5The area of region B =2That is…

Q: f(b)-f(a) Find the value or values of c that satisfy the equation b-a f(x) = 3x³ - 3x², [-1,2] =…

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Q: 1. Obtain the general solution by the indicated technique: separation of variables 1.1…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Given f(x, y) = sin(x2) + xy³, find Duf(x, y) where u is in the direction of (1, 2). What is Duf(-2,…

A: To find the directional derivative of given by function

Q: Find the slope and the equation of the tangent line to the graph of the function at the given value…

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Q: Consider the function f(x) whose second derivative is f''(x) = 3x + 8 sin(x). If ƒ(0) f'(0) = 3,…

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Q: 12 Find sin 2x, cos2x, and tan 2x if tanx = - 5 sin 2x cos 2x tan 2x 0 0 0 00 X and X terminates in…

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Q: Suppose that f(x, y, z) = x²yz - xyz³ is a function of three variables. 1. Find the gradient of f(x,…

A: The given function is; f(x,y,z)=x2yz-xyz3.

Q: Consider the following. f(x, y) = By y. y=3x-x² 0 D y=x (a) Express the double integral "fb" PLC (2,…

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Q: Find a power series representation for the function. (Give your power series representation centered…

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Q: Consider the solid λ bounded by the xz-plane, the yz-plane, the plane z = −1, the plane x+y = 3, and…

A: Let's find the value of W.

Q: Problem 2 Consider the function f(x) = x³ 4x² +10. Find the x- coordinates of the local extrema.…

A: We have given function  fx=x3-4x2+10 Derivative of the function is given as  f'x=ddxfx…

Q: 16. Determine lim f(x) if the given function is x→2 f(x) = 2.², 82r, if if x 2 x

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Q: Suppose that you have open a saving account with initial deposit of $ 5000, you continue to deposit…

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Q: Question 6 Which of the following techniques is best to use to evaluate the given integral? A e 3+e…

A: Given, ∫ex3+e2xdx

Q: 4. 3 2 (D+D²_5D+3) y = 0

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Q: Calculate 25 j by writing it as a difference of two sums and using one of the Power Sums formulas.…

A: To find:- ∑j=76250j

Q: Use polar coordinates to set up and evaluate the double integral JJ f(x, y) = 5arctan, R: x² + y²…

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Q: Find the slope passing through the two given points. 1.) (-4,-3) and (-7,-7)

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Q: 1.1. Evaluate the following integrals: a. ²x dx b. (2x+3)√2x-1 dx

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Q: Determine whether the integral is convergent or divergent. 100 (x - 6)³ 8 S² O convergent O…

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Q: Find the equation of the line tangent to the graph of f at the indicated value of x.  f(x)= 17e^x…

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Q: limg-5 5-x 2-√x-1

A: The Solution is given below:-

Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

A: Given query is to find the antiderivative of the expression.

Q: y"" y'=sin(3x)

A: The given differential equation is:y'''-y'=sin(3x)

Q: Perform the subtraction. E4816-C8416 E4816-C841616 (Simplify your answer.)

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Q: Determine if the following series converge or diverge. If convergent, find the sum. You must show…

A: a.

Q: Question One (a) Let U = 3i-j-4k and V = -2i+4j-3k. Show that U-V is commutative but U x V is not.…

A: “Since you have posted multiple questions with multiple sub parts, we will provide the solution only…

Q: Find the area under y = x(e)^(-x)^(2) for x > 1

A: The given curve y=xe-x2 We have to find the area under the curve for x&gt;1.

Q: Find the linear approximation to the function f(x) = 3x + 4 at a =3, [0,6].

A: Linear approximation formula f(x) = f(a) + ( x-a )f'(a) Given f(x) = 3x + 4

Q: Graph the line with the given point and slope. Using the format of graph in picture. 1.) (-6,4);m=…

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