Question:2 Find domain of following functions S(x, y) = In(e*+e") arctan(x+y) а. f(x, y) = b. ( x² – y? х - у is (x, y) < 2 if (x, y) > 25

Q: 4. The two differentiable functions f(r, g) and g(r,0) satisfy the identity 9(r, 6) = S(r cose, r…

A: Given two differentiable function are f(x,y) and g(r,θ)  such that g(r,θ)=f(rcosθ,rsinθ) given that…

Q: 1. cosh z= cosh x cos y + i sinh sin y sinh z = sinh x cos y + i cosh x sin y.

A: According to our guidelines we are supposed to answer only one question, since you have asked more…

Q: artial Differentiation. If u = In(x² + y²) and z = sin ollowing: eva a²u ay?

A:

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A: Given  f(x) = sin2x - x1 - cos x,x&lt;0tan x + cos xx - sec x,x≥0 We have to check the continuity of…

Q: VARIATION OF PARAMETERS 1. (D^2+1)y= sec tanx

A: We have to solve by variation of parameters.

Q: 1. Find the tangent line to the graph (4-x)y? = x³ at the point (2, 2). 2. Find the tangent line to…

A: Equation of tangent line

Q: Derivatives: using (4 step rule). 1. q(t)=10 + 5t – 1? 2. s(x)= 3-x ,2 4. f(x)=sin3xcos 3x 5.…

A: Note :As per our guidelines we are supposed to answer only one question if there are multiple…

Q: y" +y = 3 sin 21 +t cos 21

A:

Q: lim (1, y)→(0, 0) (r + y +9)e-1/(z²+v²)

A:

Q: 1 e function f (x) = ,x E [-27, 2nt| is continuous on: 1-cos x

A:

Q: 1. lim cot-1 (e*). 2. lim sech (ln x) x-0 S(x) = sech z

A:

Q: 9) Find all relative extrema in the interval (0, 2π) for y = x - cos x

A: Here we have to find the relative extrema.

Q: •tanx √1+1² 0 1+e' sec ³x 1+etanx If f(x) = A B C D -dt, then f'(x) equals 1+tan²x 1+e' tan.x In…

A: Solved below

Q: Question: Differentiate the following functions 4 1-cos2x a) Y= , by chain rule. 1+cos2x) b) Y=…

A: Using chain rule of derivatives,  fgx'=f'gxg'x Yx=1-cos2x1+cos2x4 ⇒Yx=2sin2x2cos2x4⇒Yx=tan8x

Q: 3.44 3. Test for homogeneity f (x, y) tanx-sec²x - cosy

A: Question : Test for the homogeneity f(x, y) = tanx - sec²x - cosy

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A: (Cos(x-y) + cos(x+y)) /2.cosx.cosy =?  We know that cos(x-y) = cosx.cosy+sinx.siny…

Q: ..LH.S.-R.H.S. - HW/ Prove that: (1) 1-tanh x=sech'x

A:

Q: f(x)=\arctan (1-x),[0,1]

A:

Q: + h - cos/ cos What is O -1 2 O 1 O Limit does not exist

A: Given: limh→0cos3π2+h−cos3π2h Formula: cosx+y=cosxcosy−sinxsiny                 limh→0sinhh=1,…

Q: cOS X COsy dx + (1- sin x siny) dy of from X = 0 the urrve y sihx

A:

Q: 1. If z=ln (x-y) +tan (x+y) find zxx and zyy

A: Given: z=lnx-y+tanx+y  ……1

Q: 2x x² + 2x+1 1 +C X+1 A arctan x+ 2 + C (x+ 1)2 2ln|x+1| – 2 + C © 2ln|x+1|+ X+1 1 +C X+1 -arc cot X…

A:

Q: u – 12uzx = 0, e00, with the boundary conditions Uz (0, t) = 0, Uz (T , t) = 0, t>0; and the initial…

A: As per the question, we will solve by separation of the variable method.

Q: Two spacecraft are following paths in space given by ri = (sin(t), 1, t²) and r2 = (cos(1), 1 -1,r).…

A: Use rate of change of temperature

Q: 1. Find the tangent line approximation T to graph of f at the given point. f(x) = Vx, (2, vZ) 2.…

A: Since we can only answer one question. We'll answer first question because exact one wasn't…

Q: Integral proof Prove the formula f coth x dx = In |sinh x| + C of Theorem 7.6.

A: Consider the provided integral, ∫cothxdx=lnsinhx+C Show that the left hand side is equals to right…

Q: uy constants. Show that lim,y(t) = 0 for every solution of this equation.

A:

Q: cosh (T- i) = %3D e cosl i e sin 1 + e- cos 1 + i e- sin 1 e cosl i e sin 1 + e-TI cos 1 ie- sin 1 2…

A: We know formula of coshx in term of exponential form

Q: cos x- cos y X, =0, y,=0; sin |x|-sin | y | x, 0, yo=0; B) f (x, y)= %3D %3D r) f (x, y) = %3D %3D…

A: As per bartleby guidelines, for more than one question asked, only one is to be answered. Kindly…

Q: EXAMPLE 4 Find the arc length for the curve y = 2x2 In(x) taking Po(1, 2) as the starting point. 16…

A:

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A:

Q: Displacement of a structure is defined by the next equation for a damped oscillation y = 9ekt cos ot…

A: Given - Displacement of a structure is defined by the next equation for a damped oscillation y =…

Q: ysiny limy-»o (y+siny)²

A:

Q: i. y = sinh-1 (x), ii.y = cosh-1 (x),x > 1 iii.y = tanh-1 (x), |x| < 1 %3D

A:

Q: Prove Jhab sinY Tim lim e-1 lim Sin y ニ ン と Siny S iny

A: Given,            limx→0sinxex-1=limx→0ex-1sinx=limx→0esinx-1xTo find : Prove the given limits.

Q: cos e - sin 0 Find a closet rank-1 approximation in the l² norm to A = %3D sin 0 cos 0

A: Consider the provided question, The l2 norm or Forbenius norm(FN) is the square root of the sum of…

Q: sin(2(a? + y?)) 2(x2 + y²) f(x, y) sint as (x, y) → (0,0). Assume that polynomials, exponentials,…

A: Use limit rule to calculate

Q: O lim メーや 2X-5 /メ -V-オ-2 V x +3 ar conditioning. メーろ 2-x2 ulim メー→/2 | lim 4) "Sina-Cosxsinx; メーO…

A: a.limx→42x-53=2×4-53=1 b. limx→-3=x+4--x-2x+3since numerator is not zero, while only denominator is…

Q: 2х x2 +2x+1 A 2ln|x+1| + +C x+1 1 - + C x+1 В -arc cot X 1 +C x+1 C arctan x+ D 2ln|x+1| - (x+1)?

A:

Q: sinh(4 x) Differentiate the given function y = cosh(4 x) – 6 1– 6 cosh(4z) a) cosh(4 x) – 6 6 b) O…

A: Solve for the derivative

Q: 1 2-r 1 3. Evaluate the integral: dydx. 1+x + y

A: Question is solved.

Q: f(0) = 1 + cos²0, [T/4, ] %3D

A:

Q: etermine if g is differentiable at x = 0 if -1 COS if – 1 0. x + cos x

A: Differentiable

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A:

Q: cos() y = 4 – t, z = CoS x = 3t, dz/dt using the chain rule. Assume the variables are restricted to…

A:

Q: FINO THE PARTICUCAR SOUTUON OF THE DIFFERE NTIAL EQUATION -スx =e + hx t子x-9 dx² -2x dy e AT X=0,9=0…

A:

Q: sin 3x . [T] lim S.M; x→0 ; ±0.1, ±0.01, ±0.001, ± 0.0001 sin 3x sin 3x X -0.1 а. 0.1 е. -0.01 b.…

A: Evaluate the limit for x→±0.1limx→-0.1sin 3xx=Sin 3x-0.1-0.1                    =-Sin0.3-0.1…

Q: Limits with Three VariablesFind the limits in Exercises 25–30

A: Dear student, since you have posted multiple questions, as per our policy we will answer first…

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: