• The Doman of f(x) = 4-Vx is 1. (2, co) 2. [-2, c0) 3. [2, 0) 4. [-2,2]

Q: FCx): 2x-5xナ3 find f'co).

A: We are solving the first question and for the next question post the question again and also mention…

Q: Let f(x, y) = x² + 5y². (a) Find f (5, 1) and f,(5, 1). fx(5, 1) fy(5, 1) =

A: Find

Q: Differentiate the function. f(x) = sin(x) In(4x) f'(x) =

A: ddxu(x)v(x)=v(x)ddx(u(x))+u(x)ddx(v(x)) ddx(sin(x))=cosx ddx(ln(ax))=aax=1x…

Q: (4-х, XS0 10) Determine if the function y(X) = 3x, is differentiable at x =0. x>0

A:

Q: Let F(x, y, z) = x3³yz² - 6x²yz + 9xz - 2y³z. Find F Fxyz' 3x²yz² - 12xyz +9z+ x³z² − 6x²z − 6y²z +…

A: This question is based on Partial Derivative.

Q: Let f(x,y) = x² - 3xy-y². Compute f(4,0) and f(4, − 3). - f(4,0) = (Simplify your answer.)

A: If you have any help please let me know in comment box and then I will help you.

Q: Suppose f(x, y, z) = xyz + 2xy + 2² · Compute the following values -(2,8₁16) - (-2,-8, 16) (1,-1,0)…

A: We have to find functional value.

Q: Translate Q (0, -8) using (x, y) → (x - 3, y+ 2). Your answer: O Q'(-2, 5) Q' (3, - 10) O Q'(-3, -6)…

A: The transformation is, (x,y) ------> (x-3, y+2) So, (0, -8) ------> (0-3, -8+2)

Q: The function u(x, y) obeys, 8²u Ərəy = -2e

A:

Q: = Evaluate S₁2₁,22,23] f (2) dz where 21 = −i, z2 = 2 + 5i, zg 5i and f(x + y) = x² + iy

A:

Q: Let f(x, y) = (- (3z + y))°. Then

A:

Q: 8(x) 48. f(x) 2 - x' In Exercises 51–60, show that f(g(x)) = x an dom x - 1 g(x) of 51,fx) = 2r + 1,…

A:

Q: Consider the following bijections on R: f (x) = - g(x) = x – 7 Then (f o g)¯'(x) =

A: Given, fx=-x,gx=x-7 Find the value of f∘g-1x.

Q: What is r' (x) when r(x) = In ? Select the correct answer below: O Pu) = - Sr+1 O rw = - Sr+1 x) = !…

A:

Q: Let m ∈ Z, m ≠ 0. Congruence modulo m is an equivalence relation: (a) For all a ∈ Z, a ≡ a mod m…

A:

Q: Letr' (t) = (3 + 4t, cos(t), 6e³t) and 7(0) = (7, 2, 5). Determine r* (t). r(t) = ([ (..)

A:

Q: (2xy + 3x²)e +(x² – 2yz + 2y)e,y- (e² + y²)e, olan f(x, y,z)

A: Given

Q: Find the value of fr and fy at (1,-1) when 4 +5x² + 3y². xy f(x, y) =

A: Given: fx,y=4xy+5x2+3y2We need to find fx and fy at 1,-1.

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.