Find dy any ay of Ay of y =f(x) = x² +x at x= 10 when ax =0.1.

Q: Find the linear approximation L(x of the function f(x) =V1– at a = 0. L(x)=mx+b where m is - and b…

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Q: A r&r.'Find y as a function of t if 9y" – 24y' + 7y = 0, and y(5) = 3, y' (5) = 8.

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Q: Find the directional derivatives of the convex function f(x) = max{−5x + 3, 2x + 1}.

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Q: true or false :  There exists a function F of two variables x, y such that dF = (x − y)dx + (x +…

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Q: Find y as a function of tif y(0) = 2, y'(0) = 3. y(t) = 0 16y" + 104y' + 169y = 0,

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Q: Differentiate fx) with respect to g(x) of yx= xsiny

A: To find the derivative

Q: The function z is defined by z(x, y) = x y-3 y Find A z and dz when x= 3, y= 5, Ax = - 0.04 and A y…

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Q: Show that the function y = x1/2, x > 0, is strictly concave

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Q: Find the linearization L(x) of f (x) = tan x at a =

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Q: Suppose X1, X2 ∼ Unif(0, 1) and are independent. Let Y = min(X1, X2). Find fY (y).

A: We have given that X1,X2∼U(0,1)Objective :To find the  PDF of Y=min(X1,X2)

Q: The function f(x) = Ei-1 Cix;| is piecewise linear and convex. True O False

A: Step:- 1 Convex piece-wise Linear: - A function f: ℝn→ℝis a convex piece-wise linear if there exist…

Q: Find fzzz for f(x, y) = x²y².

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Q: let r (t) = The y component of r' (5)

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Q: n For each nEN, consider x = with x ER+. Define the sequence {gn} by x (a) (b) A = [1,2) CR. (1)…

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Q: Consider f(x,y) = xe*y +. Find fx , fy and fxy. y

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Q: Find fyx for f(x,y)=exln(y)

A: Given : fx,y = exlny

Q: f (x, y) = (x² + y²)5

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Q: First write the function y = Vx2 +1 as a composition of y = f(u) and u = g(x), and then dy apply…

A: y=x2+1y=f(u), u=g(x)To find:dydx

Q: Consider f(x, y) = xy(²-x²) x² + y² 0 if (x, y) = (0,0) if (x, y) = (0,0) . Show that fay(0,0) = 1…

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Q: Find y as a function of a if y(0) = 2, y(0) = 3, "(0) = 7. y(x) = y"9y" + 18y = 0,

A: y'''-9y''+18y'=0y(0)=2, y'(0)=3, y''(0)=7To Find: y(x)

Q: Let g(x) = | F(t) dt, where fis the function whose graph is shown. y f 12 1 (a) Evaluate g(x) for x…

A: Given The given integral is  and the given graph is  Apply formula  The area of the right angle…

Q: Find a simple closed curve C with counterclockwise orien- tation that maximizes the value of f t* dx…

A: Given an integral. We need to find the C that maximises the value of the integration.  Let's start.

Q: Calculate Vf when f 3x 2- y z' + 4x'y + 2x - 3y - 5 at the point (1, 1, 0).

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