4. If f is a function from A to B, and S and T two subsets ofA, show that: f(S UT) = f(S)uf(T) f(SnT) Cf(S)n f(T) (a (b %3D

Q: 10 If f is a continuous function and F'(x)=f(x) for all x € R, then x)dx=?

A:

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

A: The solution is given as

Q: If f(x) = In(tanh(2æ)), then f'(x) is %3D Select one: O a. coth(2a)sech (2r) O b. 2 coth(2a)sech…

A: Given: f(x) = ln(tanh(2x))…

Q: Consider the piecewise-defined function f defined by S 7– 2x? if x >1 f(x) = 19 – 4x if x < 1 Find…

A: This means f(x) is continuous at x=1

Q: Let X and Y have the joint p. d. f. $2x for 0< x < 1; 0 < y < 1 otherwise f(x, y) = Then P (X + Y <…

A: Given  Information: Let X and Y are two random variables with joint pdf, fx=2x  , 0&lt;x&lt;1,…

Q: hich z ∈ C the function e^(1/z) is holomorphic?

A:

Q: 19 Let y be a function such that y(1) , where Y (s) = L{y (t)}. If it is known - that: d ds s4…

A:

Q: here r jl and nl is a function of x or k i m very confused can u please explanion

A: The function is,................ j2x=π2xyi+12xη2x=π2xNi+12x

Q: If functions ƒ(x) and g(x) are continuous for

A:

Q: Show that if w = ƒ(s) is any differentiable function of s and ifs = y + 5x, then∂w/∂x - 5 ∂w/∂y = 0

A:

Q: Q2: Expand f(x,y) = [sin (x y³)]² about (5, 1).

A:

Q: 2. (i) Consider the following function of two choice variables Z-f(x,y) Write down the first order…

A:

Q: 4 Suppose that f(1) 3, f(4) = 5, f '(1) = 4, f '(4) = 2, and f " is continuous. Find the value of xf…

A:

Q: Let f(x) = ()*)**, x = 0,1, is p.d.f then P(x = 0) = %3D

A:

Q: 1. Suppose f is a function which satisfies f(x + y) = f(x) + f (y) for all x,y e R. What is the…

A: Let f is a function which satisfies f(x+y) = f(x) + f(y)  for all x,y∈R   f(x+y) = f(x) + f(y) ,   ∀…

Q: 3 B Consider the following function, z= x -2xyty't yn Lind the alues of ag Ddz,z,when redgyel dy 6.

A: Given : z = x2 -2xy + y3 + yw

Q: If f:R→R is a continuous even function, then | F(x)dx is necessarily equal to -5 O10 O Cannot be…

A: A function is even if f(-x)=f(x)

Q: 1. If F(x)= = ² e²² et² dt, find F(1) and F'(x). ez

A:

Q: If f(3) = 15, f' is continuous, and I f'(t) dt = 24, what is the value of f(4)? %3D

A: In this question, f is a primitive function and we have to find f(4). So I am providing the…

Q: 1. Find grad f for the given function below. Ax, y, z) = 5xy + 3yz – 4zx

A:

Q: 17. Let f(x, y) = x'y4. Use Eq. (4) to estimate the change Af = f(2.03,0.9) – f(2, 1)

A: You have to just put the value in the function and proceed....go through the solution

Q: 1. Apply the Parseval's identity to the function f (x) = x, –n < x < n

A:

Q: 3. If f(x, y,z)= In *yz +e tar's="), find f,,fy and f. . хуz

A: we have to find the partial derivative

Q: 5. Show that the function h(x, y) defined by 1 if a? + y? 1 is discontinuous.

A: We can solve this using R.H.L ≠ R.H.L

Q: my (4) writy => p = - pgyox + f(x) — (8) =) - At yah (8) - (9) gives: telli Patru = - pghcoix + f(x)…

A: The equations are provided as: P=-ρggcosα+f(x)    …(8) and Patm=-ρghcosα+f(x)    …(9). We need to…

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: Please see picture

A: Introduction:Here, MX (t) denotes the moment generating function (mgf) of the random variable X;…

Q: 5 Show that the function h(r, y) defined by if r +y? < 1 h(x, y) 0; if r +y 2 1 is discontinuous.

A: For continuity of 2 variable function L.H.L=R.H.L=Function value at (x,y). limx→a+,y→b+…

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: Which of the following tatements is true about a mooth function f at (a, b) it ² (a, b) c, fax (a,…

A: f has relative maxima at (a, b) if D&gt;0, fxx(a,b)&lt;0 f has relative minima at (a, b) if D&gt;0,…

Q: Find and for the functions: of Əx af ду bren 2. f(x, y) = x² − xy + y² X (x² + ² noitonut sil 4.…

A:

Q: consider a function f:lo 11-» R. and etheruoise iff RELmaan amntegrable DY not A=3+1

A:

Q: Suppose f(x, y) = xy² + 1. Compute the following values: f(0, 1)= f(1,0)= f(0, 0)= f(2, 1)= f(t,…

A: we have given f(x,y)=xy² +1. We have to find the following . Now for f(0,1) we can put x=0 and y=1

Q: Suppose z = ƒ(x, y), where x and y are functions of t. How many dependent, intermediate, and…

A: It is observed that z=fx,y is function of x and y.

Q: 2. Consider the three functions below: S(z) = 2z S(z) =r S(x) = 2"

A: fx=2x,fx=x2 and fx=2x (a) Take the value of x as -2,-1,0,1,2,3. x fx=2x fx=x2 fx=2x -2 -4 4 14…

Q: If f(x) is a function satisfy ing f(x+a)+ f(x)%=D 0 for all c+b x e R and constant a such that f(x)…

A: The least positive value of c is 2a.

Q: 19. If f is continuous and o f(x) dr = 20, find | #f(x*) dx af(r²)dr

A: given ∫09f(x)dx=20  and we need to find ∫09xf(x2)dx=?

Q: '18 6. If f is continuous and f(x) dx = 16, find f(2x) dx. %3D

A:

Q: , Consider the function f(x, y) = x'y + y – 27y. f has v at (3/3, 0). f has ? at (0,0). f has ? v at…

A:

Q: If f(1) = 13, f' is continuous, and f'(t) dt = 28, what is the value of f(4)?

A:

Q: (2) Is the function f(x) : R → R, sin a 1 ifa # πh,k & Z, ifa = Tk, k ε Z f (x) Borel measurable?

A: Consider the given function, fx=1sinxifx≠πk,k∈Z1ifx=πk,k∈Z   Thus, the given function have infinite…

Q: If f(2) = 14, f' is continuous, and f'(t)dt = 23, what is the value of f(5)=? %3D

A: Given :

Q: 2. If f(x, y) is a function of y only, then S" S fdxdy Si fdy. %3D

A: Given query is to find statement is true or false.

Q: Suppose that f is a continuous, strictly increasing function on [0, 1] and that the •1 range of f is…

A: Here given function is continuous and strictly increasing function on [0,1]

Q: Find the value k that makes the function continuous. S ka?, f (æ) = x > 2 ka + 4, г 2

A: Given thatfx=kx2         x&gt;2kx+4    x≤2We have to find value of K for which function is…

Q: If f(2) = 13, f' is continuous, and | f'(t) dt = 27, f(6)? what is the value of Answer:

A:

Q: 3. Let # 0, 0, r = 0. f(x, y) = Find f.(x, y), fy(x, y) at all points. Leave your answer as a…

A: We need to find differentiation of f(x,y) with respect to x and y.