4, 0 5 (f * 9)(t) =

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Q: 1.If f(x,y) cos(4x-2y)+ln(y² -2x) find £xy fx fxy,

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Q: Find the length of the curve e^x / 2 + e^-x /2 between x=0 and x=1

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Q: The critical point of the function* f(x, y) = x² + 5y² + 2 cos x

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A: The solution is given as

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Q: (d) Finally, show that the conditions for the theorem are not satisfied for the initial value…

A: (D) here fx,y=y13 differentiate it with respect to x ∂f∂x=13y-13dydx initial condition y0=0

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A: Let us consider, F^(x,y)=F(F(x,y),y)  On applying the implicit function theorem , can get a solution…

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Q: Consider the R² – R function f defined by f (1, y) = 2² – 6x +3y² - . (a) Find all the critical…

A: For critical points we need to find first order partial derivatives of given function and substitute…

Q: 3 36 Consider a fumetion f whose first and second derivatives are f'(x) and f"(r) = 5/2 (1r² + 1)"/2…

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Q: 1. If f(x, y)=3x' cos y– y sin x– 2.x In y- yln x-4x²y, find ôf ôf d²ƒ _ô²ƒ

A: According to question given thatf(x,y)=3x3 cosy-y2 sinx-2x ln(y)-y ln(x)-4x2y

Q: Let f(x) 18xe 18 %3D (a) f'(x) : (b) Solve f'(x) 0 to determine the critical values of f.

A:

Q: 3 62 what is 13 | f(t) dt? f(x)dx = 3 6.

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Q: 3. Find the linearization L(x) of the function at a. F(x) = Vx, a = 4

A: Use the formula for the linearization of a function about any point.

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Q: 2z Forz> 0, 순(/"m(P + 1) a) In (t³ + 1) dt For x > 0,

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Q: 2. Find frxz for f(x, y,z)= z² e³xy

A:

Q: 2. Given f(x, y) = 12x2x³ + 3y² + 6xy. (i) Find critical points of f. (ii) Use the second derivative…

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Q: Solve the initial value problems for x as a functionof t. (t + 1) dx/dt = x2 + 1 (t > -1), x(0) =…

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Q: Q4) The critical points of the function f(x, y) = 8y³ – 12xy + x³ O (0,0) and (1,2) O (0,0) and…

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Q: Determine the value of the Wronskian W(y1, y2) of y" - 2y + 1 = e2*(x + 1) if x-0.2 by using…

A: Given, y''-2y'+1=e2xx+1. The objective of the problem is to obtain the value of the Wronskian if…

Q: x+2 32 dt at x = 4. 2+t 6 Find the linearization of f(x) = 3-

A:

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: d) The function +(xy)-r*r2y) exp G 18xy is homogencous in of degree X and

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A: Hey, since there are multiple subpart posted, we will answer the first question. If you want any…

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A: Consider the provided question, According to you we have to solve the part (b), (c) and (d). (b)

Q: (x² + 4) dy 山 3. y(2) = 0

A: we know that ∫dxx2+a2=1atan-1xa+C,  where a>0 see below the answer and calculation

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Q: (b)Assume that f(x) is a function of the form -x-1; when -T < x <0 f(r) = when 0 <r < T Prove…

A: For the solution of the problem follow the next step.

Q: If sin(x) f(x)= V2+t2 dt tan(x) and g(y)= f(x) dx g" (4) Then is equal to V5 - 2 V3 - 2V3 11 E- 2V3…

A: Given:            f(x)=∫tanxsinx2+t2dt  and g(y)=∫1yf(x)dx

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Q: Use the method of variation of parameters to solve the initial value problem x'=Ax+ f(t), x(a) = x₂…

A: We have to find the solution x(t) using the method of variation of parameters.

Q: lim, f(x)= 0, then | f(x)dx diverges

A: Statement:  limx→∞ f(x)≠0,  then ∫1∞ f(x) dx   diverges.

Q: 3. Find the critical points of the function f(x, y) = 4x2 + 9y2 + 8x-36y + 24 and use the second…

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Q: 22) The critical points of the function F(x,y) = x³ + 3xy + y3

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Q: 9) A function y(x) is increasing and has upward concavity on the interval [-2, 3]. Would a…

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Q: x+2 Find the linearization of f(x) = 6 - 21 dt at x=4. 1+t 6

A: Given a function f(x) at x=4 We have to find the linearization of f(x) at x=4 For solving this 1st…

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Q: Solve the initial value problems for x as a functionof t. (t2 + 2t) dx/dt = 2x + 2 (t, x &gt; 0),…

A: t2+2tdxdt=2x+2⇒dx2x+2=dtt2+2t Now integrating on both sides, we get…

Q: find ∇f at the given point. ƒ(x, y, z) = x2 + y2 - 2z2 + z ln x, (1, 1, 1)

A: Given function is fx,y,z=x2+y2-2z2+zlnx and point=1,1,1

Q: V Solve usıng variaton of parameters or reduction of order (D²+1) y = tan

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Q: 11) Find a function y-f (x) that satisfies both conditions: d - 6x -4x+5,f(-1) =3 dx %3D dy 2 3 ==+…

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Q: What is dufferential equation of x'=4x-y and y'=-4x+4y when t=0, x(0)=1 and y(0)=1

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Q: 1. Find and classify the critical points of f (x, y) = 6xy – 4x³ – 3y?

A: Critical points of f will occur: fx and fy is o. Given equation is f(x,y) = 6xy-4x3-3y2…

Q: 4) Let g(x,y) = 2x² + y² – x²y. a. Find the critical point(s) of g. b. Use the second derivative…

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Q: Let y : R → R be the real-valued function defined on the real line, which is the solution of the…

A: The differential equation is given as Y’  = -xy + x , y(o) = 2 From the type of the problem we can…

Q: 13. Prove that the function 2x 1 dt t F(x) is a constant on the interval (0, ∞ )

A: The student has specifically asked for the solution to Question-13. Hence, that question is solved…

Q: 25 p1 3) Compute f(x)f'(x) dx where f(x) =x +2, using the Composite Trapezoidal 2 rule, your results…

A: