Q3) For what values of a and b are (-x² + a , y = { xsin-+1, 0 < xs: bx³ + 2 , Continuous at every x ?

Q: is continuous at x=3, f (-1) =6 ? + a, x # 3 3b, x 3 ontinuous at x=2? - x > 0

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Q: Suppose that f [a, b] → R is strictly increasing, i.e., that if x₁ < x₂ then f(x₁) < f(x₂). Explain…

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Q: 3. If f is continuous and | f(x) dx = 10, find af(x*) dr. Give proper reasoning.

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Q: Q3) For what values of a and b are ax + 2b , y =x? + 3a -b, (3х -5, 0 2 Continuous at every x ?

A: Equate at given value

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A: Let's find.

Q: Let ƒ(x, y) =(x2-y2)/(x2+y2)  for(x, y) ≠ (0, 0). Is it possible to define ƒ(0, 0) in a way that…

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Q: ɔ that h is a continuous functi (x2 — 2, х < 6 h(x) 3= 7х + a, х 6

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

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Q: Q3) For what values of a and b are ax + 2b , y = x? + 3a -b, 3x-5, x 2 Continuous at every x ?

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Q: 2. f(x) = Vx – 1 at x = 5

A: Function is continuous and differentiable both at x= 5.....for detail...go through the solution

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A: In these question , we can check where the function is continuous . Check where the function is…

Q: Show that f(x) = is uniformly continuous by definition on the interval (-1,1) . 4 - *

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Q: Is there a continuous function such that - f: [1,2] U [3,4] → R - f(1) * f(4) < 0 - f(x) not egual 0…

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Q: Find all values of c such that f is continuous on (-∞, ∞). S 4– x², x c с 3 (smaller value) C =…

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Q: Find all values of c such that f is continuous on (-o, 0). { 7- r, /(r) – (smaller value) (larger…

A: f(x)=7-x2,x≤cx,x&gt;c

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Q: If f (s Continuous then on -fex) True or felse?

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Q: (b). Show that iff= u+iv is analytic in a region S and u is a constant function (i.e., independent…

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Q: (2) Are all entire functions differentiable on D?

A: Here we check whether given statement is true or false. Are all entire functions differentiable in…

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: Find a value of k making h(x) continuous on [0, 5]. kx 0 < x < 2 x + 1, 2<x < 5 h(x) =

A: The given function is hx=ekxif 0≤x&lt;2x+1if 2≤x≤5. The function is continuums. That is,…

Q: Suppose that a continuous function g satisfies: 9(z)dr = 42 and 9(2x)dz = 12. | z9(32°)dz. Find

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Q: how (in terms of  − δ) that a function f : R 3 → R defined by f(x, y, z) = (2x + 3y + 4z) is…

A: Solution of given problem is followed by

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Q: that makes y continuous but not differentiable by writing the required procedures to that If: X≥0…

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Q: 4. Give an example of a continuous function f : (0, 1) → R that cannot be uniformly approximated by…

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Q: Suppese that X, X and that f is continuous. Show that f(X,) 1(X). Show w that ETLJY

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

Q: Find a value of k making h(x) continuous on [0, 5]. kx , 0 < x < 1 h(x) = x +3, 1<x < 5

A: Given: hx=kx,0≤x&lt;1x+3,1≤x≤5 given function will be continuous over 0,5, if it will be continuous…

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

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Q: ... uavarasvo vr-vv, find the x-values (if any) at which f is not continuous. Which of the…

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Q: Show that the function f(x) = csc(x) is not uniformly continuous on (0, pi/2]

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Q: Q\ Use appropriate functions to guarantee that (). x sin if x # 0 h(x) = 0, if x = 0 is continuous…

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Q: Find aland U so that the function S 7z³ – 3x² + 7, z -2 is both continuous and differentiable. al =

A: To Determine: fins a and b so that the function is continuous and differentiable given: we have a…

Q: Suppose that f(1) = 5, ƒ(4) = -8, f'(1) = 4, f'(4) = -2, and f" is continuous. Find the value of |…

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Q: Q-2-for what valne of b is x+2b gex)=- 2 x²_b b-3 2. Continuous at every x ?

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Q: Find all values of a and b that make -a - x, x< -2 /(x) = { Vx + b, bx² + 1, -2 Sx<1 x21 continuous…

A: Given:             fx=-a-x,            x&lt;-2bx2+1,    -2≤x&lt;1x+b,        x≥1

Q: alue of c that makes the following function continuous: S 1+ cx if x 2.

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Q: Show that if f: I¬R where I is open interval in R, is differentiable at point p in R then 'f is…

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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

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

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Q: For what values of a and b is ax + 2b, g(x) = {x? + 3a - b, 0<xS2 3x 5, %3D - continuous at every x?

A: The given function is gx=ax+2b,        x≤0x2+3a-b,  0&lt;x≤23x-5,           x&gt;2. For the given…

Q: Let f be in R[a, b]. Prove that -- f is in R[a, b] and ∫a b -- f(x)dx = -- ∫ab f(x)dx.

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Q: II. Find all values of a and b that make -а - х, f(x) = {bx² + 1, Vx + b, x<-2 -2 sx<1 x21…

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Q: Q3) For what values of a and b are (-x² +a, y ={ xsin - bx3 + 2 , 0 <x<: Continuous at every x ?

A: Given information: The function is y=x2+a          x≤0xsin1x+1   0&lt;x≤1πbx3+2       x&gt;1π…

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

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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: Q3) For what values of a and b are -x² + a , x Continuous at every x ?

A:

Limits of Multivariable Functions

Multivariable calculus is an extension of single variable calculus. It involves several variables instead of just one. Assume there is an open set containing points (x0, y0), let f be a function defined in that open interval except for the points (x0, y0). The multivariable limit of this function as it approaches the points (x0, y0) and is denoted as: