8. Find constants a and b such that the function (18, f(x)={ax+b, -3

Q: Suppose that f(x, y) = at which %3D - {(x, y) | 3 < x < 4, 3 < y < 5}.

A: we have ,  f(x,y)=xy at which (x,y)|3≤x≤4,3≤y≤5 we have to calculate,  ∫∫Df(x,y)dxdy

Q: Find the values of a and b that make f continuous everywhere. x2 4 if x 3 a = b =

A:

Q: The set of functions {sin nx}, n = 1, 2, 3, ... , is %3D orthogonal on the interval [ -n, n]. Show…

A: Given- The set of functions sin nx, n = 1, 2, 3, ⋯, is orthogonal on the interval -π, π To Show-…

Q: What three conditions must be met for a function ƒ to be continuous at the point (a, b)?

A: Continuity at points: The points of continuity are the points where a function exist and has some…

Q: Find the values of a and b that make f continuous everywhere. x2 – 4 - if x 3 a = b =

A: Given that,

Q: Examine if f(x) = x3sin(1/x) is uniform continuous on the interval (0,2]

A:

Q: Find the constant a such that the function is continuous on the entire real line. Ax) = {2x2, (ах -…

A: Given that , the functionfx=2x2,x≥1ax-7,x&lt;1We have to find constant a such that the function is…

Q: Show that f:Z-->Z ; f(x)=x+2 is invertible

A:

Q: The function f(x,y) =26-2x²-y² is continuous at point (2, -3). .A True .B False

A: The objective is to determine whether the statement, " The function fx,y=26-2x2-y2 is continuous at…

Q: Find the interval(s) wheref (x) =vx+ 2x+6 jis continuous. A) [2, 6] B (-*, *) C) -6, 6] D) [0, -)

A:

Q: In approximating one real root of f (x) = on (1, 3), which endpoint of the interval is constantly…

A:

Q: Show that f(x, y) = point (5,-3). 3x+2y x+y+1 meets the three conditions for continuity at Add-ins…

A:

Q: Suppose that ƒ'' is continuous on [a, b] and that ƒ has three zeros in the interval. Show that ƒ''…

A:

Q: Show that f (x) = is not uni form continuous on (0,3) -3

A: To prove that 1x-3 is not uniformly continuous on 0,3

Q: Prove that f(x) = [[sin²(2log r)– 3 sin ( 2logt)+2] dt %D 1. Cannot be decreasing any where,

A: To prove that f(x) can not be decreasing anywhere, where f(x) is defined as…

Q: Use Theorem 2 to show that 3, if x <-10 2, if – 10 sxso F:R → R,F(x) = -2, if 0< x< 10 -3, if x2 10…

A: so we have to show that given function is discontinuous at 2 and -2 (a)   Discontinuous  at -2…

Q: The interval on which f(x) = 5 – 12x2 – 4x³ is concave up is: (-∞, –1) © (-1, 00) O (-0, 1) • (1,00)

A:

Q: 1. f(x) = x2- 6x + 3 is continuous on the interval [- 3,2].

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: f continuous everywhere. f(x) =   x2-4/x-2      if x < 2

A: Given fx=x2-4x-1if x&lt;2ax2-bx+3if 2≤x&lt;32x-a+bif x≥3 fx is continuous everywhere. Aim: Find…

Q: Determine two unique values of θ in the interval [0,2π), such that                    sec (θ) = 2√3/…

A:

Q: Use the definition of the hyperbolic functions to prove that 2cosh (x)-1=cosh(2x).

A: As per the instruction, we will be answering only the first question. For (a),      2 cosh2(x)-1=2…

Q: Determine if f(x) = x4sin(1/x3) is uniform contuinius in the interval f : (0,∞) --> R

A: Some facts related to uniform continuity of function: A  function f is uniformly continuous on…

Q: Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

A:

Q: Suppose f(x) = π − 2x − cos x. (a) Show that f is strictly decreasing on R. (b) Hence, justify that…

A:

Q: 14) Test the secies for convergane divergence or 2. (-1)"

A:

Q: ) Verify the continuity of the function f(x, y) 26– 2x -- y at the point (2,-3).

A:

Q: 5. Verify first that the Intermediate Value Theorem applies to the indicated interval and find the…

A:

Q: Find all values of a and b that make -а - х, x<-2 f(x) = {bx? + 1, Vx+b, -2<x<1 x21 continuous…

A: The function is given by: f(x)= -a-x , x&lt;-2           bx2+1 , -2≤x&lt;1         x+b   , x≥1 Also…

Q: Suppose that f(1) = 2, f(4) = 8, f '(1) = 4, f '(4) = 3, and f " is continuous. Find the value of xf…

A:

Q: 5. Show that the functions x, x² interval [-1,1]. x are mutually orthogonal in the -

A:

Q: Prove the interval [0, infinity) is closed but not bounded

A: Consider the provided question, We have to prove that the interval [0, ∞) is closed but not bounded.…

Q: See image below.

A: We subtract x from both sides

Q: Find the slope of the line tangent to the graph of the relation (5x - 34e)(y +5e) = e(x - 10e) at…

A: The given relation is, 5x-34e(y+5e)=e(x-10e) taking ln both sides,

Q: Suppose that the functions f and g are defined throughout an open interval containing the point x,,…

A:

Q: Suppose that f: R² R is a function given by y³ x² + y² f(x, y) = 0 for x = y = 0. Show that f(x, y)…

A:

Q: Show that f (x) =++1 1 - is not uni form continuous on (-1,0)

A:

Q: Consider the relation x2z2 = arctan (xyz) + 4, which defines z as an implicit function of x and y,…

A:

Q: 5. Show that the functions x,x? -,x³ -x x are mutually orthogonal in the interval [-1,1].

A:

Q: If f is continous on [0,1) ,then f has absolute minimum on(0,1) True or false?

A: Extreme value theorem says that, if a function is continous on a closed interval [b, a] , then it…

Q: let Peas be delimed by Xく2 3-X I5 fixo continuous V= 2 2.

A: A function is continuous at a point if it's left hand limit is equal to right hand limit and both…

Q: 8. Use the c, 8 definition to show that fAx) = x? +1 is continuous at

A:

Q: Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

A: Intermediate Value Theorem: It states that if f is a continuous function whose domain contains the…

Q: 8) Assume that 2 + Va if x >1 if x < 1 f(x) = Determine whether or not f is continuous at x = state…

A:

Q: 2. Use the Intermediate Value Theorem to prove that the equation e* = 4 - x³is solvable on the…

A:

Q: Show that the equation x - 17x +c = 0 has at most one solution in the interval [-2, 2]. Let f(x) = x…

A: The given equation is : fx=x3-17x+c The given equation has at most one solution in the interval…

Q: Show that the function is differentiable by finding values of ε1 and ε2 as designated in the…

A: Given function is fx,y=x2+y2.…

Q: Suppose that the function f: R → Ris continuous and that its image f (R) is bounded. Prove that…

A:

Q: Apply Definition 1.4 of Chapter IV to show that the function f(x) = 3x + 2 is integrable on the…

A:

Q: is: The interval of continuity of flx) = /2x – 10 OA[5, +0) OB.(-5, 51 OC(-0, + x) OD(-00,-5)

A: Function f(x) is continuous on interval [a,b] if it is continuous at every point.

Q: If f(z) is analytic with constant modulus show that f(z) is constant u=3x²y+2x²-y³-2y²

A: To Proof :-  If f  z is analytic with constant modulus , show that f  z is constant.  Given :-  The…