1. Compute the first, second, and third derivative of a. f(x) = x² In(x+1) b. h(x) = x² sin x

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Q: In y dy dx 1 xy 20.

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A: NOTE: As per our guidelines, I have solved the first problem in the solution (3rd question). If you…

Q: Let D={(x,y) | x2 +y² <49}. Let f(x,y)=V49-(x²+y²). J| f(x,y)dA <343T Select one: True False

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Q: I3D Find the first partial derivatives of the following function. f(x,y)%3D3×Y

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Q: 30 25. 2 k(k – 2)(k + 2). - k=1

A: "Since you have asked multiple questions, we will solve first question for you. If you want any…

Q: Use the chain rule to find the derivative of f(z) = 4/10z5 + 4x4 Type your answer without fractional…

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Q: 2x 3, Use the limit definition of derivative to show that f(x) is differentiable at x2 – 3, r > 2 x…

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Q: Find the gradient of the function at the given point. g(x, y) = 18xe/x, (18, 0) vg(18, 0) =

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Q: Compute the first partial derivatives of the fol f(x.y) = 4 – tan 1 (3x?+2y?) -1(3x2 +2y)

A: f(x,y)=4-tan-1(3x2+2y2)partial differentiation w.r.t xfx=0-1(3x2+2y2)2(3×2x)…

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Q: If the marginal cost function is given by c'(x) = 3x + 4x+ 3, then a general expression for the…

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Q: b)Find the average value of f(x) = x3 – 1, 0<x<4

A: We can find the average value of the function as below.

Q: What are the first four terms of the sequence n+1 00 3n-1 n=1 Select one: 3 2 4 3 O None of the…

A: Given problem:-

Q: Divide. (4x – 17x- 8) ÷ (2x²-5) Remainder Write your answer in the following form: Quotient+ 2x-5…

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Q: SI sin(x) dydx. valuate the integral, show work.

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Q: Find the Taylor series for f(x) centered at the given value of a and the interval on which the…

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Q: The entire graph of the function f is shown in the figure below. Write the domain and range of f as…

A: From the graphDomain is set of x values where functions is definedDomain : (-4,-3) ∪[-1,2)

Q: 2) Solve triangle ABC if a = 4,b=7,c 6. Round your answers to two decimal places.

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Q: Use the chain rule to find the derivative of 4(6æ° – 2")" You do not need to expand out or multiply…

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Q: EXERCISES 2: Find all the local maxima, local minima, and saddle points of the functions 1. f(x, y)…

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Q: 7 n2+ 3 n+ 2 lim 7 9 n2+ 2 18 n- 00 Select one: O True O False

A: limn→∞7n2+3n+29n2+2

Q: Evaluate the given integral by making an appropriate change of variables.   where R is the…

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Q: The demand function for a product is modeled by  p = 400 − 4x,   0 ≤ x ≤ 100,  where p is the price…

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Q: 49 2s2 +16 121

A: This is a problem related to inverse laplace transform. Based on the general formula we will answer…

Q: 3(x +2)" In(n) 2. Consider the power series What is the centre a of this power series? What is n=2…

A: Solve the following

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Q: Identify whether the following functions are continuous or not. Write your solutions on a separate…

A: Find your answer below

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Minimize…

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Q: Find the limit. 300 lim er

A: limx→∞ x300ex

Q: By volume, one alloy is %60 copper, %30 zinc, and %10 nickel. A second alloy has percents of %50,…

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Q: dy Find by implicit differentiation a. ペt=e4 b. Jxy=xy+| Sinx t 2 cos 2y=I %3D C-

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Q: The functions y1 = ex and y2 = e-3x solutions for the homogeneous DE: are both y" – 9y = 0. Then,…

A: y''-9y'=0Since y1=e3x  , y2=e-3x are the solutions of homogeneous DE  Then complementary function is…

Q: Solution: Step 1: The function f(x) needs to be verified continuous at the open interval (-1, 1) by…

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Q: How/Find the solution for the equaton

A: Note:- These are multiple questions and according to our company guideline we can do maximum one…

Q: Justify your answer whether the following functions are continuous or not at a certain point or…

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Q: hction given as J(E) that IS a Simplify the expression f(x + h). f(r + h) = f(r + h) – f(x) Simplify…

A: Given : f(x)=-2x+1.

Q: Find the AREA of the region enclosed by r =2+2 sin 0. A. 27 В. 4т С. 6т D. 8T

A: Here we have to find the area of the region enclosed by r = 2+2 sin(theta) .

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Q: Sketch the region of integration for the integral sin(x) dydx. Draw the region on a piece of paper…

A: see below the answer and explanation

Q: 2. Is the function f(x) =² continuous on the closed interval [-1, 1] ? Draw its graph illustrating…

A: Given problem:- Is the function ƒ(x) = 3/x continuous on the closed interval[−1, 1]? Draw its graph…

Q: A. For each of the following functions, find the indicated derivative using the definition. 4. f(x)…

A: Let's find.