Find y as a function of t if 3y′′+31y=0 y(0)=7, y′(0)=3

Q: Consider the curve in the xy-plane represented by the two equations below. The slope of the line…

A: Given: x=et……1y=te-t……2 where t≥0   To find: Slope of line tangent at x=3

Q: (b). y" – 3y + 2y = u1(t), y(0) = 1, y(0) = 1, where u1(t) is unit step function and u1(t) = u(t –…

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Q: 4 - Find the direction A in which the function f(x, y) = x cos y + y sin x decreases most rapidly at…

A: We have to find the direction A in which the given function decreases most rapidly.

Q: The function g(t) = \t| is differentiable at 0. True False

A: Given that g(t)=|t|We can write it as:g(t)=t   , t≥0-t , t<0

Q: 4) The position function of a particle is given by F(t) = (t², 5t, tť² – 2t). When is the speed a…

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Q: 7. Find the linear approximation near (2, 0) of f(x, y) = 3x e¯3ªy.

A: To find the linear approximation for the given function.

Q: Find the linearization L(x)of the function at a .

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Q: Find y as a function of t if y(0) = 4, y(0) = 1. y(t): = 64y" - 144y + 81y = 0,

A: Given: The characteristics equation is             64m2-144m+81=0⇒m=--144±-1442-4· 64· 812·…

Q: Find y as a function of t if y" – 10y' + 21y = 0, y(0) = 7, y(1) = 4. y(t) = Remark: The initial…

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Q: A. If r = r(t) represents the position function at time t of a certain particle, then what do you…

A: first derivative of position gives- velocity

Q: 1. Calculate the derivative dy/dx for the plane curve defined by the equations…

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Q: Use differentials and the graph of f to approximate (a) f (1.9) and (b) f (2.04). To print an…

A: To calculate the approximate value of a) f(1.9) and b) f(2.04)

Q: f(x, y, z) = e2* +e3y + e4=

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Q: Find the quadratic approximation at (0,0) for f(x,y) = e^(x+y) * (xy-1).

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Q: Find the derivative of the given function at P. (3, 3, 3) in the direction of u = 3i + 4j f (x, y,…

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Q: 19. The slope of the tangent to the curve (x2 + y²)² = 4.x²y at the point (1, 1) is 3 3 (a) - () – 1…

A: We have to find slope of the tangent to the curve x2+y22=4x2y at the point 1, 1. We know slope of…

Q: Find the linearization of f(x) = 3+ S" sec(t - 1)dt at .2 END x = -1

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: YouTrylt 2 Find the linear approximation of the function f(x,y) =In(x- 3y) (7,2) at and use it to…

A: Please rate and feel free to ask any query about any part of the question.  Thanks

Q: 3. Find the interval on which the curve of y= 2 1+3t+t² dt is concave up.

A: Second derivative is positive.

Q: 4. Find the orthogonal trajectories of the family of curves y=Ce*™ +10

A: We have to find the orthogonal trajectories of the family of curves

Q: Compute the discriminant D(x, y) of the function. S(x, y) = x' + y* – 6x – 2y + 1

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Q: Find x' for x(t) defined implicitly by x+t°x+t -8=0 and then evaluate x' at the point (-2,2).

A: x3+t3x+t4-8=0Differentiate w.r.t…

Q: Find the vertical trace of the function at x = 1: g(x, y) = cos√x² + y²

A: Definition : Consider a function z=f(x,y) with domain D⊆R2. A vertical trace of the function can be…

Q: Verify that the indicated function y = p(x) is an explicit solution of the given first-order…

A: This question can be solved using the concept of derivatives.

Q: Find the differential of the function. z = 7t − 7/t2

A: zt=7t-7t2

Q: Determine the coefficients a, b, c, and d, so that the curve y = ax' + bx² + cx + d have critical…

A: Since you have asked multiple questions, as per our policy we will answer first question. Please…

Q: Find the equation of the line tangent to fƒ(æ) = e² (x² + 3x) at the point (–2, –2e¯²). O y = -3e-2…

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Q: Find the linearization of the function f(x): L(z)= ab a --4x-5 va a न 4x+3 at z=-1 sin (a) E

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Q: The function f(z) = 1 has a poles at z = %3| ez – 1

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Q: 5. Determine whether the functions y, and y2 are linearly dependent on the interval (0,1). Yi = 1+…

A: Linearly independent of the function. Using Wronskian

Q: The x- coordinate of the point on the graph of y = Vx-1 at which the tangent line is perpendicular…

A: slope of tangent of the curve y=x-1 is dydx=12x-1 slope at (x1, y1)dydx=12x1-1=m1if (x1, y1) is the…

Q: Find the linearization L(æ) of the function at a. f(z) = V7, a = -8 L(x)

A: We can find the linearization as below.

Q: Find the orthogonal trajectories of the given family of curves x^2 + y^2% D c^2. *

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Q: 6. Find where the velocity of a particle is zero if its position function is x(t)= t In t

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Q: Find the equation of the line tangent to y 8xe" at x = 1. O y -8e = 16e(x – 1) O y - 8e = 8e(x – 1)…

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Q: - Use Euler's method to estimate y(3) given y(0) = 1, and y' = x -. Use steps of h = 1

A: use euler method for finding the y(3)

Q: If y = x(x – 1)* then y' at z = 2 is equal to

A:

Q: A) Find the linearization of the function at the given point. f (x, y) = 1+ y ln (6 – xy), at (5, 1)…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Find the Giniindex for the lorenz curve L (X)= 0.3X + O=7X 11

A: Given the Lorenz curve Lx=0.3x2+0.7x. Find the Gini index of the Lorenz curve.

Q: Question 12 Find the linear approximation of the function f (x, y) = 2x – y + a²y - near the point…

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Q: Find an equation for the level surface of the function f (x, y) = ln (x² + y²+ z²) that passes…

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Q: for the function f(Z) z²-2z find the (z+1)° (2 t4) residues at singular points.

A: The residue of f(z) is solved below

Q: 1. Find the stationary points of the following functions. (a) f(x,y) = x²y+ 2y² – 2xy + 6 - (b)…

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Q: 5. Find y' at the point (0, e) where xy² + In(x² + y) = 1.

A: Find y' = dy/dx At point (0, e)

Q: Find the linearization of the function at the given point f(x,y)=-10x+8y-9 at (-7,4). A.…

A: I have appended the formula used in the solution part

Q: Find the orthogonal trajectories of the family of curves ey + 2x2 = k.

A: Given,  ey+2x2=k

Q: Consider the curve in the xy-plane represented by the two equations below. The slope of the line…

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Q: Find y as a function of t if y(t) y" + 2y + 10y = 0, y(0) = 8, y'(0) = 9.

A: The given DE is: y''+2y'+10y=0 The auxiliary equation of the given DE is:…

Q: Find the linearization L(x) of the function at a. f(x) = Vx, a = 16

A: