2. Show that X H→ In x is increasing on (0,0) and that In 1 = 0:

Q: Find the antiderivative of: x*+1 (n+ 1)2 [(n + 1) In x – 1] if n± -1 x* In x dx = z (In x)² + c if n…

A: Find the anti derivative.

Q: A more detailed version of Theorem 1 says that, if the function f(x, y) is continuous near the point…

A:

Q: 1. Show that c(t) = (e¬t cos t, e-t sin t), 0 <t <∞ has finite length and calculate its valu

A:

Q: expand e cos y near (17) 1, by Taylor's Serios method

A:

Q: 4 18. Evaluate the indefinite integral / dx. 3 X,

A: Given integral to find ∫4x3dx To integrate this first take the constant out 4∫1x3dx Applying the…

Q: A more detailed version of Theorem 1 says that, if the function f(x, y) is continuous near the point…

A: Explanation- Given that, The initial value problem is- ydydx=x-1;  y0=1 By simplifying it further,…

Q: b) Show that the “energy function" E(x, y) = 5 + is non-increasing along the solution, i.e., using…

A: (b) The objective is to show that the energy function  is non increasing along the solution, that…

Q: 2 3 Evaluate the integral f S(x² + y)dydx. 0 1

A: Here given two variables in Integration

Q: 2. Let f(x, y, z) = In(x² + 2) + y²e#* - cos(2yz). Find fzyz-

A:

Q: Let z = cosh t. Find the differential dz when t = In 3 and dt = 0.2 O 4/3 O 4/15 O 8/15 O 1/3

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Q: Find the linearization L(x) of y = e In(x) at a = 1. L(x) = %3D

A: Given a function f(x)=y=e3x ln(x) To find the linearization L(x) at a=1 The linearization L(x) is…

Q: A more detailed version of Theorem 1 says that, if the function f(x, y) is continuous near the point…

A: Explanation-  Given that, The initial value problem is- dydx=x2-y2 ; y0=1 Here, The function is-…

Q: 5.) Suppose z = f (x, y) , where x=x(t,r) and y= y(t,r). Assuming all the functions involved have…

A:

Q: A more detailed version of Theorem 1 says that, if the function f(x, y) is continuous near the point…

A:

Q: Evaluate the double integral: ∬ 4y/(1+x2)dydx y runs from 1/2 to 2 x runs from 0 to 1

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Q: H.W- Compute y() with y-J=-8(Sinx+cosx) y(TT)=0,4(TT) = -8 %3D by @ Taylor series

A: The given problem is to solve the non homogeneous linear differential equation with given initial…

Q: Suppose that (r, y) = e-v and o(In 2, In 2) = 1. Please use the technique of linear approximation to…

A:

Q: A more detailed version of Theorem 1 says that, if the function f(x, y) is continuous near the point…

A:

Q: Find the solution of the differential equa­tion that satisfies the given boundary condition(s) .  f"…

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Q: Let y 5x²8x + 4. If Ax = 0.1 at x = 1, use = differentials to estimate Ay Ay ~

A:

Q: 8. Evaluate the integral S xydx from x=3 to x=6 when x = 6cos0 and y = 2cose A. 9/7 B. 9/3 C. 5/3 D.…

A: Topic:- integration by substituting

Q: A more detailed version of Theorem 1 says that, if the function f(x, y) is continuous near the point…

A: The given initial value problem is ;    ydydx = x-1  with  y(1) = 0 We have to determine the…

Q: ==4-x² - y² for which z ≥ 0 with upw= rcle x² + y² = 4 that forms the boundar

A: The Stoke's theorem states that ∫CF·dr=∬S∇×F·dS Where z=gx,y and dS=-gx,-gy,1dxdy.

Q: (4)Evaluate the definite integral (a)S(1 + sin x )£x 1/2 (b) [ (2t + cost)dt -*/2 x +1

A: As per the Guidelines, I will answer the first 3 Integrals. For the fourth one please repost the…

Q: A more detailed version of Theorem 1 says that, if the function f(x, y) is continuous near the point…

A:

Q: 1. Consider the function z = x In(1+ y²), if x 2-t and y= Vf, use an appropriate form %3D dz at t…

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Q: Suppose that z = xy² and x and y are differentiable func- tions of t with x =2,y = when t = -1. Then…

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Q: Use at least two methods to prove that dr/dt=0 when r=√x2 + y2, x=α cos t, and y=α sin t if α is a…

A: First method   r=x2+y2r=(α cost)2+α sint2            since x=α cost and y=α sint  =α2cos2t+α2sin2t…

Q: Suppose that a body moves through a resisting medium with resistance proportional to its velocity v,…

A: (a)

Q: Let f (x,y, z) = xyz2 + 1 and suppose that x(t) = 2 – t, y(t) = In(t), and z(t) = 3t. df Use the…

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Q: Compute the first-order central difference approximations ofO(h^4) of t function of y at x = 1h =…

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Q: of Let f (x, y) = tanh-¹(x-y) with x=e" and y= usinh (t). Then the value of dt (u,t) =(4, In 2) is…

A:

Q: 9. Let f(x) x In(10) Find the most general antiderivative. F(x)

A: Given data÷ So,we need to find F(x).

Q: A) If w = 2 y et* – In z where x = In(t² + 1), | dw y = tan-1 3t and z= e3t. Find by Chain Rule dt

A:

Q: e) Suppose that W= √√x² + y² + z², x= cos 0, y = sin 0, z = tan 0. dw T Use the chain rule to find…

A: According to our company's guidelines I can only answer (e), since (e) and (f) are not inter…

Q: Integrate the fuackion f=g regian bonndel by y the en6* y-o ver

A: The function is fx=xyThe region is bounded by y=x, y=6-x, y=0

Q: 6) Find most general antiderivative of the fxn ) f(2) = secx (secx +tane) Secx +tanx, = secx COS X

A:

Q: 2. Set up an integral to find the exact length of the curve defined by 1 f(x) = 1 In r 2 - 4* where…

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Q: A more detailed version of Theorem 1 says that, if the function f(x, y) is continuous near the point…

A:

Q: 2 Evaluate the improper integral 4x e dx, if exists. 8.

A: Given that,           ⇒           ∫-∞2e4x dx   ,   if exist             ⇒         find the…

Q: (4z + 5)² tan zy= + dr Cos z

A:

Q: 3. Use chain rule to find given w = Vx2 +2y2 + z² and a cos (st), y = -2s In t ane 2 = 3s?Vt. 3s2Vt.

A: Follow the procedure given below.

Q: A more detailed version of Theorem 1 says that, if the f f(x, y) is continuous near the point (a,…

A: Given: (15). dydx=x-y (16).dydx=x-y

Q: If u(x, y) = 2 tan-1 2 and v= In (x² + y?) , prove that: a2v = 0 дхду dx2

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Q: integral of C(1-e^(-bt)) with the initial time being 0

A: Let's find.

Q: se Euler method to compute ys for the DE yy'=2 x for y(1)=3

A: Euler's Method