Let f(x) = V30 – x and g(x) = x? – x. Then the domain of fogis equal to a, b] for a = and b =

Q: is The antiderivative of the function f(x) =. 2x а. 2 In x + c b. 1

A: Givenf(x)=12xAntiderivative of f(x)=?Antiderivative is nothing but integral.

Q: find f given f (z, y) = e + 2ry 4y at (0,3)

A: Topic- partial differential

Q: 2. If f (x) = Sn* et? 0, dt, find f'(x) V2t+sect

A: The solution is given as

Q: Suppose that f(x) is an antiderivative of f(x) = V1 + xt. Express JoV1 + x* dx in terms of F and…

A:

Q: Suppose that F(x) : = 7 r1) | f(1) dt, where %3D V3 + u6 du. f(t) =

A: We will use the Newton-Leibnitz theorem twice in the following solution and then evaluate at x = 2

Q: Use the linear approximation of f(x) = at r = 0 to approximate f(-0.1). 1+r

A: Use the linear approximation of f(x)=1/(1+x) at x=0 to approximate f(-0.1).

Q: Consider the function f(x) = a²e15z. f(x) has two inflection points at x = C and x = D with C < D…

A:

Q: Q1 If f(x,y, z) = 2 x²y + ez+ Vz Inx %3D Find fr fy and f2

A:

Q: Find the antiderivative F(x) of function F (x) = 3 such that F(1)=0. r4

A: Anti derivative: ∫F(x)dx = f(x)

Q: Use the definition of differentiability to show that f(x, y) = y² – xy+5x is differentiable…

A:

Q: Consider the function f(x) = 5a°+ 5x® – 10x4 – 6. Enter an antiderivative of f(x)

A:

Q: Determine the linear approximation of f(x) = x² at x = 1. a. y= 2x +1 O b. y = 2x - 1 O c. y=- 2 x-1…

A: Given: f(x)=x2, x=1 To find: Linear approximation at given point.

Q: a. Find linearization of f(x) = Vx +1 at x = 7. b. Using your answer above, estimate V8.1.

A:

Q: of and dy For the function f(x,y) = In (8x + 9y), find - - of

A: partial derivative of two variable functions

Q: Suppose z is a function of x and y, and csc Vr² + yz = z"esin. Solve for dz and

A: A multivariable function is a rule that connects two or more variables. The partial derivative of a…

Q: Given f(x, y) = et" Y° – a°y°, show that fæy = fyx· 93 fyæ- %3D

A:

Q: Show that f (x) = 1 − |x| satisfies the conclusion of the MVT on [a, b] if both a and b are positive…

A:

Q: Suppose f(r) z2 + sin z and F is an antiderivative of f that sausfies F(T) 0. Then F(2) = ( -1)

A:

Q: let x has the p.d.f (11e-11x 0 < x< ∞ 0. W f(x) = Find m.g.f and prove that E(x) = M,(0)? %3D

A: We want to find the Mx(t) and E(x)

Q: Given that f(x, y, z) = xy + z and x = s2, y = st, z = t2, find the composite function.

A: To find the composite function.

Q: For what value of a is

A: Given           f(x)=x2-1    ,  x&lt;32ax       ,   x≥3

Q: Find the following for z = f(x, y) = x? +5x2y3-y. az %3D ax

A: FOLLOW NEXT STEP

Q: find given f (x, y) = eª + 2xy² – 4y at (0, 3) af dy'

A:

Q: For function f(x,y) to have maximum value at (a,B) IS 1) rt – s>0 and r0 and r>0 3) rt – s?0 and r>0

A: for function f(x,y) to have maximum value at (a,b) is rt-s2&gt;0,r&lt;0

Q: Which of the following is NOT differentiable at x=4? f(2) =+4 x - 4 ... A x + 4 ... f(x) = (x – 4)²…

A: If a function f(x) is differentiable at x=k then f'(k) must exist in the domain. If x=k is not in…

Q: Consider the function g : Z x Z → Z × Z given by g(x, y) = (x+ 3y, 2x – y). Is g injective? Pr -…

A:

Q: For what value of b is Sx, g(x) bx?, x 2 -2 X<-2 continuous at every x?

A: The given function is gx=x,x&lt;-2bx2x≥-2. Assume that g is continuous function.

Q: For f(z) = 2z', find ip using the definition,

A: The limit definition of a derivative of a function, f(x) at a point, x=a is given by .

Q: Show that the subtangent of f (x) = ex is everywhere equal to 1.

A: Formula to find the subtangent of the function helps to find the required subtangent. Derivative of…

Q: Find whether the function F-(* - y')i + (v² – 3x)j + (=* - xy)k is irrotational.

A: A vector field F is called irrotational if curl (F) = 0.

Q: Find f, and f, for f(x,y)=y In (3x +4y). fx fy

A: When the partial differentiation is done with respect to a specific variable, then all other…

Q: The range of the finction f(x, y) = In(-x² -+1) is %3D None of these O (00:0] O [0; +0) O [0;1]

A:

Q: Consider the function F whose criterion is = / dt. 1+ t2 F(x) sena When determining dF/dx the result…

A:

Q: For y=f(x)=x²-2x+7, find dy and Ay, given x=4 and Ax= -0.2. dy=(Type (Type an integer or a decimal.)

A: Use formula and put value

Q: 10.Show that F(x, y) = (1 + xy)e*yi + (ev + x?e*y)j is conservative and find a function "f" such…

A:

Q: If Tn,0(x) = ao +a¡x+ a2x² +.. he function f(x) centered at x = %3D -) True p) False

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Find the antiderivative F(x) that satisfies the given condition. F'(x) = 4ex - 5x²; F(0) = 10

A:

Q: Consider the function f(x) = 7x° + 9x° – 9 - 9. Enter the antiderivative of f(x) + C

A: T

Q: Suppose that f(x, y) = e 42? - ly + 7z + 2y then find the discriminant of f.

A:

Q: Consider the function f(x) = 9x° + 9x' – 10a? – 4. An antiderivative of f(x) is F(x) = Ax" + Bxm +…

A: Given: fx=9x8+9x7-10x2-4

Q: Determine the linear approximation of f(x) = x* at x = 1. а. у %3D 4x - 3 O b. y=- 4 x - 3 О с. у-…

A:

Q: Consider the function f(x) = 6x' + 8x5 – 10x³ – 6. %3D - Enter the general antiderivative of f(x)

A:

Q: Suppose that f(0) = 1, ƒ(0.5) = 2.5, f(1) = 2, and f(0.25) = f (0.75) = a. Using trapezoidal rule…

A:

Q: Find the linear approximation of f(x) = Vx at xo = 27.

A:

Q: Show that the function d: RxR → R defined by d(x, y) = √x-y

A:

Q: (3) If | f(x) dx exists and c is a real constant, prove that f(2) dz = / f(x + c) dz. | {(x+c) Vel

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: Let F(x) be the antiderivative of F ‘(x) = -2x + 6, with constant 0.  Determine F(x), and then…

A:

Q: [a, b]. If F(x) is an antiderivative of f(x), for real numbers ¤) + k]dx is equal to

A:

Q: Consider the function f(x) = 4x° + 7x® – 9z³ – 10. %3D Enter the general antiderivative of f(æ)

A:

Q: 0If z-x"f), show that xZ+JZy=mZ.

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.