Find the following limits xy (a) lim (x,y)→(3,2) x + y

Q: Use the given information to find the exact function value. Simplify your answer as much as possible…

A: Given that the expression

Q: Exercise: Solve the equation d³y dy dx3 +3d²y +3d+ y = 0 dx2 dx

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Q: 29 Find the area under the curve y = from x = 1 to x = t. Evaluate the area under the curve for t =…

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Q: Express the given rational function as a sum or difference of simpler rational functions

A: The required answer is given below Explanation:Step 1: Step 2: Step 3: Step 4:

Q: find all the values of a such that y=xa is a solution of yII-12x-2y=0

A: The objective of the question is to find the values of 'a' for which the function y = x^a is a…

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A: The objective of this question is to find the first five terms of the sequence defined by the…

Q: Find the angle of intersection, in radians on the domain 0 <t≤, to two decimal places.

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Q: Parameterize x(y) = √√y+5y using y = t Ans=

A: The parameterization of x(y)  using  y = t  is  x(t)=t​+5tExplanation:Given expression is…

Q: Evaluate the integral.

A: 1. 34​π​2. 72π2​​Explanation:1. Given:∫3​1​3​​1+x28​dxFirst we need to take out the constant, we…

Q: Evaluate the integral

A: 1.  3(arctanx)3​+C2.  earcsinx+CExplanation:

Q: Evaluate the integral. } [(51²) i+ [(5t²) i+ (5)j +(3t+3)k] dt 0 [(51²)+(5) (5t²) i + (5)j +…

A: The Basic Integral formula is given as follows

Q: For the function f(x) = 4+ 12x² − x³, find the local extrema. Then, classify the local extrema using…

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Q: Find a general formula for f("). f(x) = (x+4)-1 (Use symbolic notation and fractions where needed.)

A: Given that the function

Q: Evaluate fim x+

A: We will find the limit.

Q: Let w = xy − 3yz + xz, x = st, y = e³t, z = t² - Compute მი -(—2, 2) : = მs მო -(-2, 2): = at

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Q: You are told that f(x) is everywhere continuous, passes through the point (8,5) and that f(x)+8 lim…

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Q: On what interval(s) is the function f(x) = x - 4x³ both decreasing and concave up? (Enter your…

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Q: u × v = (1, 1, 0), ux w = (0, 3, 1), V X W = (2, −1, 1)

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Q: The demand curve for original Iguanawoman comics is given by q =  (398 − p)2 50       (0 ≤…

A: Ep = - 0.2 (has been rounded off) Explanation:

Q: Imagine you're at a movie theater where the screen is 36 feet tall, mounted on the wall so its…

A: The given figure Let AB=x ft

Q: Find X1 and X2- -2 - 4 X1 -2 3 x2 H + 19 -9 3 17 X1 X₂ = 38

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Q: A direction vector of the line passing through the points A (3,-1,-2) and B(-1,2,1) is <-4, 3,3). •…

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Q: ☐ 1. Find the volume of the solid formed by revolving the region bounded by the graphs = x² about…

A: V=5162π​Explanation:Step 1:

Q: Compute the mean, median, and mode of the data sample. (If every number of the set is a solution,…

A: The objective of this question is to calculate the mean, median, and mode of the given data set.…

Q: Using Linear Approximation, estimate & for a change in x from x-ax=& f(x)=x, a=32, b=32.4 Comider…

A: The given function is

Q: Let  f(x) = e19 − 18x^2. (a) Find the interval(s) where  f(x)  is concave up. (Enter your…

A: The answers are: (a) f(x) is concave up on no intervals, so the answer is None ( ∅ ). (b) f(x) is…

Q: An offshore oil well is 2 kilometers off the coast. The refinery is 5 kilometers down the coast.…

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Q: Find к for the space curve r(t) =2ti + (2a cosh (t/a))), a > 0. K(t)= (Type an exact answer, using…

A: Given:space curve- To find:

Q: Calculus Math Question. Please help.   Thank you

A: Derivative of y with respect to x is given below Explanation:Step 1: Step 2: Step 3: Step 4:

Q: In (x + √√x². Find the first partial derivatives of the function f(x, y) = ln(x+ 1. fx(-3,4)= 2. fx…

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Q: Estimate Ay using differentials. y = x 1/2e4x-1, a = 1, dx = 0.1 (Give your answer to four decimal…

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Q: At the start of an observation, there are 7727.8 grams of a radioactive element present. The number…

A: The value of dt/dN at N = 25 up to 2 decimal places is:(dNdt​)N=25​=50.44Explanation:Given equation:…

Q: dy Find by implicit differentiation da 5+3x=sin(xy)

A: 5+3x=sin⁡(xy6)ddx(5+3x)=ddxsin⁡(xy6)

Q: lim 4zex²+y² (x,y,z)(2,4,5) 2x² +4y²+5z²

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Q: The daily cost C' (in dollars) for a manufacturer to produce x electronic video components is given…

A: An increase of $39.44 Thank you  Let me know if you have any doubts Explanation:Step 1:

Q: Use direct comparison test or limit comparison test 00 n = 1 1 + cosn n 2

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Q: Assuming that the domain of the function is the largest possible subset of R (the set of real…

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Q: Find T and N for the space curve r(t) = (5e' cost) + (5e' sint) j + 7k. T()+(k (Type exact answers,…

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Q: Hello I am working on applications of inetgration, specifcally, surface area problems. I am…

A: Given integral-To find:Evaluate the integral

Q: Plot the points from the table below on the polar grid that follows.

A: Plot the points from the table below on the polar grid that follows.Explanation:To plot a point in…

Q: Find SS, 20 JA, R = [0,2] x [3,3] x²+1 Round H answer 10 H

A: The answer is as follows: ∫∫R​x2+1xy2​dA=9ln5.Explanation:Steps and explanations are as follows…

Q: Find the second partial derivatives of the function f(x, y) = x³ ³ + 2x²y. дх² = If 2. 3. 4. дудх…

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Q: Website Profit You operate a gaming website, www.mudbeast.net, where users must pay a small fee to…

A: explained below Explanation:Step 1:(a) Construct a linear demand function for your website and hence…

Q: Evaluate the derivative of the given function at the given point. y = 2x³-3x² + x + 8; (1, 8)

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Q: 3x3 +5y3 lim (x,y)-(0,0) x² + y²

A: To find the following limit.

Q: Consider the function z = z³y+ 30x4-7776y. Find and classify all critical points of the function. If…

A: Consider the functionTo find and classify all critical points of the function.

Q: Notice this is the graph of the derivative of g not the graph of g itself. Answer the following…

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Q: Consider the function f(x, y) = x²y + y3³ - 48y. f has a maximum f has a minimum く at (-4√3,0). at…

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Q: Find all solutions of the elation in the interval [0, 2π). cos 0-1=-1 Write your answer in radians…

A: The equation in the interval [0,2 pi).cos theta - 1 = - 1 Add 1 both sides, we get theta =0