1. Use Lagrange multipliers to find the maximum and minimum values of f(x, y) = 4x - y subject to the constraint z2 + 2y? 66, if such values exist. maximum = minimum %3D

Q: Given the differential equation у" — у' — 12у %3D 7ез^ cos(x) Determine the Wronskian for the differ...

A: Solving wronskian

Q: Determine whetherthe limit exìsts or not when a) xーヤ 3 and 6) x→-3 F(x) = 1 Vx?4 Wien x<-ろ Vg-x² whe...

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Q: (Write the answer in your own handwriting, scan and then upload the file) Q1. Prove that V = (y - z²...

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Q: Given f(x) = x- 1 and g(x) = x2- 1 Find and simplify the following 1. g {f (x)} 2. g-1(x)

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Q: Find the series' interval of convergence and, within this interval, the sum of the series as a funct...

A: Find your answer below 

Q: The n-th term in a sequence an is given by an = 3-eol (a) Is this sequence increasing, decreasing or...

A: Given:           an = 3-e-3n (a) Here:      a1 = 3-e-3(1) =3-e-3        a2 = 3-e-3(2) =3-e-6       a...

Q: Given the general solution to a differential equation and its initial conditions y(x) = C, e + C, e-...

A: Answer and explanation is given below...

Q: dy Find dx if y = « (log2(x* – 4x)) - dy dx

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Q: A function f is said to be harmonic if it obeys Af = 0, where Af V.Vf. Suppose that functions f and ...

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Q: In each case, determine whether or not the lines have a single point of intersection. If they do, gi...

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Q: Apply integration by parts: / udv = uv – - S vdu = UV sin2x – cos2x dx sin2x + cos2x

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Q: A 3" + 4) 2 +C In27

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Q: d du and dx Let f(x) T" tan 8. Find f'(x) by the formula [b"] = 6" In b dx = then by logarithmic dif...

A: topic - derivative of a function

Q: In each part, determine all values of p for which the integral is improper. Enter in interval notati...

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Q: Question Select your answer. On which interval(s) is ƒ(x) = 2 ln(x² +x – 20) continuous? (-00, –5) (...

A: Topic:- calculus  Note :- as per our guideline if more than one question uploaded than only first qu...

Q: Explain if the function is continuous or not for the given number a. if x>1 if x = 1 ,a=1 if x<1 f(x...

A: we have given function     we need to determine the continuity at a=1    

Q: Čonsider the following nonlinear programming problem Maximize Z = 36x, +9x¡ – 6x¡ + 36x, – 3x X, +x,...

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Q: 3lnx +2x*dx A 3lnx B 2r4 | 3lnx + 2r4 D E None

A: To evaluate ∫e3 ln x +2x4 dx.  

Q: csc5x cot5x dx A csc5x B esc5x 3 -csc5x 3 D csc5x E) None

A: Given  ∫csc5x cot5x dx5csc5x3    

Q: Find the area of the region enclosed by the curves  f (x)  =  4x + 15 and g(x)  =  2x + 33, and the ...

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Q: e 3* (2e 3x – 1) dx (e6x – 2)4(e3* + 1) + A 2e 3* – 1 | бх B 2e Ox – e 3x © (e3r_2)4 D D (e3+1)+ E e...

A: Please see the below picture for detailed solution. 

Q: f(x) = x2 + 7x +  5 x f '(x) =

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

Q: component form or standard basis vectors. Express numbers in exact form.

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Q: Graph the following function: y Step 2 of 2: Determine how the general shape of the graph, chosen in...

A: This is a problem related to curve sketching and it's transformation. Based on the phase shifting co...

Q: Given that xyt – 6 = 0, find dy by implicit differentiation. - %3D dx? dy dx?

A: A detailed solution is given below

Q: 12x2 Evaluate the integral: -dx 25 (A) Which trig substitution is correct for this integral? Ox = 5 ...

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Q: Find all the first partial derivatives of; glw,2, y, z) = xe2w - wyz?

A: Topic:- partial derivatives

Q: Give the degree and leading coefficient of the following function: f(x) =2x2 (4- 3x-5x3)

A: Given query is to find the degree and the leading coefficient of the function.

Q: Find  f '(x). f(x) = (x2 + 4x)(x + 3)

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Q: Let F = (6e", 5 sin(x), 8 cos(x)). Calculate div(F) and curl(F). (Use symbolic notation and fraction...

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Q: Find the lowest common multiple of 63,80,102

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Q: Integration by parts is based on what differentiation rule? Explain.

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Q: xydy – (y² + 3x²)dx = 0

A: Let, y =v*x

Q: У(4х + у)dx — 2(x2 — у)dy %3D0 - -

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Q: c =

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Q: У(xtanx + Inу)dx + tanxdy 3D C

A: The given equation is; y(tan x+ln x)dx+tan xdy=0

Q: Another - the following. a) Set up an integral for the volume a solid torus (the donut-shaped solid ...

A: (a) To set: The integral for the volume of a solid torus. Given information: radii br and aR, a=7, b...

Q: 5. Discuss real world quantities that the circulation of a vector field around a closed loop could m...

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Q: Find the extreme values of f (x, y, z) = x + 2y subject to both constraints x + y + z = 1 and y? + z...

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Q: Find the directional derivatives of the function at P in the direction of v. f(x,y) = xy P(0,1) v = ...

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Q: Find the shortest distance from the point (2,0, –3) to the plane x + y + z = 1.

A: This is a problem related to geometry part. Based on the concept of plane and point we will find the...

Q: write the following Integral as a limit (a) Determine whether the following Integrol Converges or di...

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Q: dx 1+ cos x + sin x

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Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the...

A: Here, the given curve bounded by : y=x-1, y=0 &amp; x=6       

Q: 1 Discuss the continuity of the function f(x) on the interval (0,2] and [-1,3] x2 -4

A: A function f(x) is said to be continuous in the closed interval [a,b] if→ f is continuous on (a,b).→...

Q: Use Lagrange multipliers to find the maximum and minimum values of the function f (x, y) = y² – x² s...

A: The given function is f(x,y)=y2-x2 And the given constraint x2/4 + y2=1.

Q: Question Select your answer. The function below is continuous on which of the following intervals? [...

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Q: Let g(s) = (5s – 8)*. - Then g'(s) is g'(3) is s! (s),,6 and g''(3) is

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Q: Consider tne following. (a) Set up an integral for the volume a solid torus (the donut-shaped solid ...

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Q: Determine if the given function is continuous at -1. * x < -3 - 3<x<-1 x + 7 |x – 2| f(x) = { x2 – 2...

A: determine if the function is continuous or not. type continuous if the function is continuous at a c...