Let X= {a,b} and Y={1,2,3}. Find the number n of functions from X into B

Q: How many independent variables does the function r(t) = ⟨ƒ(t), g(t), h(t)⟩ have?

A: Given that the functions f, g, and h, all depend on t. t is independent So there is only one…

Q: State the signs of f"(x) and f"(x) on the interval (0, 2). (0, 6) (7.2343146)

A: To determine the sign of 1st and 2nd derivative on the interval (0, 2).

Q: Find y as a function of x if y′′′+81y′=0, y(0)=0, y′(0)=−81, y′′(0)=−81. y(x)=

A: Given that,                    y''' + 81y'=0.......equation(1)                 y(0) =0,  y'(0) =-81,…

Q: Find y as a function of x if y" – 11y" + 28y = 0, y(0) = 1, y(0) = 5, y"(0) = 6. y(x)

A:

Q: O Find a, b to Continue The function ãt X=3 if x > 3 X = 3 ax+b flx) = 2a-b+1 bメーム+3 メく3

A:

Q: Let f(x) = 2x e¯x*,x > 0 and Let Y x2. Find G(y)and g(y). %3D

A: In this question,  we need to transform the variable in the probability density function.

Q: Plot the function f(y) =2y^2 − 2y and f(y)=12y^3-12y^2 and find the total areas of the shaded…

A: Graph of functions

Q: Use the function f(x)=x",x>0 to determine the bigger of the two numbers e' and a

A:

Q: Let F: X Y and G:

A: Given: Let F : X→Y and G : Y→Z be the two non-constant holomorphic maps between Reimann surfaces.

Q: Find y as a function of x if x'y" + 5xy' + 4y = 0, y(1) = 9, y'(1) = -2. y =

A: Solution :-

Q: Let f be a linear function. If f(−3) = 2 and f(2) = −13, find f(x).   f(x) =

A: To determine the linear function f(x).

Q: Form a PDE by eliminating the arbitrary function ø from $(x* + y² - z°.z? + 2xy)=0

A:

Q: Find a function y(x) such that 8yy' = x and y(8) = 5. y = ||

A:

Q: Find the mean of the function 1 8 (X, Y)= 5' for 0 < X s; o<Ys < X and lor< Y 2. = -1 for for all…

A:

Q: Find y as a function of x if y′′′−14y′′+48y′=0, y(0)=1,  y′(0)=8,  y′′(0)=4. y(x)=

A: The given differential equation is  y′′′−14y′′+48y′=0, Boundary conditions are y(0)=1, y′(0)=8,…

Q: Calculate L3, R3, and M3 for the following function over the interval [0,3]. f(x) = Vx + 1

A: The given function f(x)=x+1 over the interval [0,3]

Q: Find y as a function of x if y′′′−2y′′−y′+2y=0, y(0)=−8,  y′(0)=−7,  y′′(0)=−5 y(x)=

A:

Q: Find yy as a function of xx if y′′′−8y′′−y′+8y=0 y(0)=4,  y′(0)=−6,  y′′(0)=130.

A:

Q: Differentiate the function. z(y) = A/y12+Bey

A:

Q: let f(x)= x2 . Find the value c in the interval (0,3) so that fave = f(c).

A:

Q: Find the value of the constant c that makes the following function continuous on (-oo, o0). Scb+3…

A: we have to find the value of the constant 'c' such that the given function is continuous at (-∞,∞)…

Q: Find y as a function of t if 25y"- 70y' + 53y = 0, and y(5) = 8, y'(5) = 1. %3D y = %3D

A: Given: 25y''-70y'+53y=0  with the IVP y(5)=8 ,    and   y'(5)=1By…

Q: Find y as a function of x if x^2*y′′+2xy′−20y=0 y(1)=−6,  y′(1)=1.

A: Find y as a function of x if x^2y′′+2xy′−20y=0 y(1)=−6,  y′(1)=1.

Q: Find y as a function of x if y" +81y' = 0, y(0) = 4, y'(0) = -27, y"(0) = 81. %3D |

A: Given that y’’’ = 81y’ = 0 And y(0) = 4, y’(0) = -27, y’’(0) = 81 y(x) = ? y’’’ = 81y’ = 0 let d/dx…

Q: Find a function y(x) such that 6yy' = x and x and y(6) = 9. y =

A: Topic = Differential equation

Q: Find the values of the function. f(x, y) = 1 + 8xy − 2y2 (a)    f(3, 2) (b)    f(−1, 5) (c)…

A: The given function is (a) Now, to find the value of function at x=3 and y=2 (b) To find the value…

Q: Find the domain of f (x, y) = x + Y

A: Given function

Q: Find a and b so that the function 2x3 – 7x2 + 4, x -2 is both continuous and differentiable. a = b…

A: Function and its derivative mist be continuous so check the continuity at x= -2

Q: Consider the function f(x, y) = e-x²-y² defined on the rectangle -2<xs 2, -1 <y < 1.

A: In this question, we find the absolute maxima and minima by using suggested steps.

Q: IS Tepresent A. Make a table for f(x). B. Make a table fo y y

A: We will find the table.

Q: 19ver. Find y as a function of x if a?y" – 7xy' + 16y = 0, %3D y(1) = –5, y'(1) = –4. y =…

A:

Q: Find y as a function of a if y(0) = 2, y(0) = 3, "(0) = 7. y(x) = y"9y" + 18y = 0,

A: y'''-9y''+18y'=0y(0)=2, y'(0)=3, y''(0)=7To Find: y(x)

Q: Let f(x,y) = 2* + 6xy, find f(0, – 3), f(– 3,2), and f(3,2).

A:

Q: Find the first 3 iterates of the function f (x) = 3x when xo = 2? D 5, 6, 54 D 5, 15, 45 D 2, 6, 18…

A: To find The first 3 iterates of the function f(x)=3x at x0=2.

Q: Find all functions from X = {a,b} to Y = {p,r,t}.

A: Given :- To find all functions from X = a,b to Y= p,r,t.

Q: Evaluate the function at the given values of the independent variables. = x³ + 3xy + y²; x = -1, y =…

A: z=x3+3xy+y2x=-1  and y=1 Replace the x  and y values in the given function

Q: Find a function y(x) such that 3yy' = x and y(3) = 3. y =

A:

Q: Find y as a function of x if y′′′+25y′=0, y(0)=6,  y′(0)=35,  y′′(0)=−100. y(x)=

A:

Q: Determine whether z is a function of x and y + z2 = 1

A: see below the answer and explanation

Q: Find y as a function of t if 64y" - 112у + 65y = 0, У(5) %3 3, У(5) 3 6. y =

A:

Q: Let X1,X, f(r;0), where Or-1, 00 0, f(r;0) = elsewhere.

A: Given information: Let X1, X2, …, Xn is a random sample of size n taken from a probability…

Q: Find the function y(x) such that y′′(x) = 0 with y(1) = 2 and y′(1) =−1.

A: Given y′′(x) = 0 with y(1) = 2 and y′(1) =−1. y''(x)=0, with y(1)=2 and y'(1)=-1Now integrate both…

Q: Find y as a function of a if y(0) = 7, y'(0) = 10, "(0) = 36, "(0) = 0. y(x) = 0 y(4) 12y" +36y" =…

A:

Q: Find a function y(x) such that 6yy' = x and y(6) = 3. y =

A: The objective of the question is solving the differential equation.

Q: Evaluate the function at the given values of the independent variables. x² + xy; x = 5, y = 4 x - y…

A: Given : z=x2+xyx-y

Q: Find y as a function of t if 1296y" + 72y' + y = 0, y(0) = 4, y (0) = 7. y =

A: The given equation is second order homogeneous ODE has the form of ay’’ + by’ + cy = 0   The nature…

Q: Find all functions f: R → R for which f(x + y) – 2f(x – y) + f(x) – 2f(y) = y – 2 |

A:

Q: Find all functions f : R → R for which f(x + y) − 2f(x − y) + f(x) − 2f(y) = y − 2

A: We are given that f:ℝ→ℝ, which follows: fx+y-2fx-y+fx-2fy=y-2 for all x,y∈ℝ.

Q: Find the lengths of the functions of y over the given interval. y² + 1)*¨ from y = 1 to y = 3 61/3…

A: Here we need to find the length of curve

Q: Determine whether z is a function of x and y. x2z + 3y2 − xy = 10

A: Given expression:                                      x2z+3y2-xy=10   Taking half of the terms to…