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

Q: f(x, y, z) = √x + yz, P(1, 1, 3), u = (a) Find the gradient of f. Vf(x, y, z) = < (b) Evaluate the…

A: A) "&gt;&lt;2x+yz​1​,2x+yz​z​,2x+yz​y​&gt;B) "&gt;&lt;41​,43​,41​&gt;C)2815​Explanation:

Q: #ind d²y/ dx²: y(x) = tan x

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Q: Examine the function and a A point C1 y= -Incx)

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Q: Find the absoulte maximum and minumum values of the following function on the given region: (Please…

A: The absolute maximum value of(f(x,y)=x2+y2−2x+2​)on the region (R=(x,y):x2+y2=4,y=0) is…

Q: 2. A rectangular bird sanctuary is being created with one side along a straight riverbank. The…

A: Let the length of the bird sanctuary  kmLet the width of the bird sanctuary  kmThe figure of the…

Q: Find the directional derivative of f at the given point in the direction indicated by the angle 0.…

A: The required answer is 24Explanation:Step 1: Step 2: Step 3: Step 4:

Q: Use logarithmic differentiation to find the derivative of y with respect to the independent…

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Q: Use Lagrange multipliers to find the minimum value of the function f(x, y) = x² + y² subject to the…

A: We know, that

Q: Problem 1. Prove Theorem 6.14 which is given below. Theorem (Second Derivative Test). Suppose that ƒ…

A: Theorem (Second Derivative Test). Suppose that f:R→R is C3 in a neighborhood of a critical point…

Q: What does the funtion N = grad(s) mean.  What does grad do ?

A: The function N = grad(s) is a mathematical expression that is used in the field of calculus,…

Q: dy Use implicit differentiation to find without first solving for y. dx ,5ry

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Q: Find y" if y= -4 cos x OA. y" 4 cos x

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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: use the ratio test to determine the convergence or divergence of the series: the sum from n = 0 to n…

A: Given series∑n=0n=∞​(1+n)n3n​  ConvergesExplanation:

Q: Find the equation of the tangent plane to the surface x = 6x3 y3+7xy at the point (1,0, 6). z=…

A:

Q: Use Linear Approximation to estimate Af = f (9.02) - f(9) for f(x) = x4. (Use decimal notation. Give…

A:

Q: c) Use the logarithmic properties to exactly evaluate the following logarithmic expression: log (10)…

A: c. -20d. From the exponential equation, even if the value of x is a negative number, it generates…

Q: f'(x) = ƒ' (e³) = f(x) = (ln x)7

A: ∙  f′(x)=x7(lnx)6​∙  f′(e3)=e35103​Explanation:

Q: Evaluate the integral. (Use C for the constant of integration.) cos dx COS -x cos-sin()+C x

A: The given integral is .We can solve this integral by integrating by parts formula method.Integration…

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS

A: Given that A(-1,1,1)B(2,0,3)C(3,3,-4) are 3 vertex of a triangle then Side AB…

Q: Give your final answer in interval notation. Determine the intervals where the graph of f(x)=x+3/x…

A: To determine the intervals where the graph of  is concave upand concave down.Note: Since you have…

Q: Write an equation for a rational function with: Vertical asymptotes at x = -1 and x = -6 x…

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Q: Use implicit differentiation to find x³+3x²y+y³=8 dy dx

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Q: (b) Compute the frequency and probability distribution of X. x P(X = x) Frequency 50 125 150 225 300…

A: The objective of the question is to compute the frequency and probability distribution of X, where X…

Q: The differentiable functions f and g are defined for all real numbers x. Values of f, f', g, and g'…

A: Therefore, the required answers are a) dxd​(x​f(x))x=4​=3b) dxd​[f(x)g(x)​]=9112​ Explanation:Step…

Q: 1) Calculate the derivatives using Implicit differentiation au ᎧᎢ and of (TU – V)²ln(W – UV) = 1 at…

A:

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS PLS

A: A.…

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: The differentiable functions f and g are defined for all real numbers x. Values of f, f', g, and g'…

A: Answer :(a)  62   (b)  423​Explanation:For any query please ask in the comment box.

Q: 2. Consider the region S bounded by the curves 1 y=x+ and y=x- 14 a. x" for x≥1 Is the area of S…

A: The objective of this question is to determine whether the area of the region S bounded by the…

Q: Use the graph to evaluate the limit. lim f(x) 0+x -B 6 30 2 R X +30 G OA. -3 OB. 3 ○ C. 0 OD. The…

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Q: The equation of the plane that passes through the point A(1, 0, 2) and perpendicular to the vector…

A:

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

Q: The diagram below illustrates the number of moose (red curve) and wolves (blue curve) between 1960…

A: The diagram below illustrates the number of moose (red curve) and wolves (blue curve) between 1960…

Q: Solve the given integral equation or integro-differential equation for y(t). y' (t) +27 (t-v)y(v)…

A: The objective of the question is to solve the given integro-differential equation for y(t). The…

Q: Graph the function f(x) = log(x-3) + 1. Identify the domain, the range, and the equation of the…

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Q: Let the universal set R, the set of real numbers. Let A = {x = R | 1≤x6} ○ {xER|x6 } ○ {x ER 1≤ x…

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

A: An increase of $ 5600/191Explanation:

Q: 2. Find the volume of the solid whose base is the region bounded by the circle x² + y² = 9 and whose…

A: Volume = 62.35Explanation:Explanation:

Q: Σ N 3 | n² 3 2 (n + 1)²

A:

Q: The Parametric equation of the line that passes through the point A(1, -1, 1) and parallel to the…

A: Given that line passes through the point A(1,−1,1) and parallel to vector v→(1,0,1)To find:…

Q: Q2\ (A) Find the tangent and normal to the curve x²-xy+ y² = 7 at the point (-1,2).

A:

Q: Give the probability distribution for the indicated random variable. (Enter your probabilities as…

A: The probability distribution of X is shown below.x23456789101112P(X=x) 1/36 2/363/36 4/36  5/36 6/36…

Q: Use the Chain Rule to find dw/dt. dw dt = w = In x² + y² + z², x = 3 sint, y = 8 cost, z = 6 tan t

A: So, After the differentiation the final answer for the question is:…

Q: 140 CHAPTER 3 Functions tab B 49. Let f(x) = (x - a)/(x + a). (a) Find f(a), f(2a), and f(3a). Is it…

A: f(a)=0f(2a)=1/3f(3a)=1/2Explanation:Hope it helps youplease ask if you gets any doubtplease give…

Q: If f(x) = 7 sin(2x) arcsin(x), find ƒ'(x).

A: f′(x)=14cos(2x)arcsin(x)+1−x2​7sin(2x)​Explanation:Given function is  f(x)=7sin(2x)arcsin(x) We need…

Q: Use a sketch to find the exact value of the following expression. cos sin 7 25 Which of the…

A: The triangle given in (C) is used to find the value of cos(sin−1257​). The value is…

Q: lim Vn!

A: Substituting stirlings approximation into the expression:limn→∞​nnn!​​=limn→∞​nn2πn​(en​​)n​…

Q: The voltage V in a simple electrical circuit is slowly decreasing as the battery wears out. The…

A: Please see the explanation Explanation:Step 1:

Q: Please help with Calculus 1 Question. Thank you.

A: dxdy​=x​2​+x36​ Or dxdy​=x2x​​+x36​ (Note: These two are just the same or…