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

Q: Q3 Limit 4xy78 Consider f(x, y) lim (2,y) (0,0) f (r, y)? What is O No limit Ò 78 O cos 0

A: As per guidelines we have to solve one question

Q: MY NOTES Find the x-values (if any) at which fis not continuous. Which of the discontinuities are…

A: Given: a) fx=lnx+1,x≥04-x2,x&lt;0 b) fx=10-8e9-x,x&gt;910-89x,x≤9

Q: 7. For continuous functions on [0,1], 1/2 | f(x) | dx < | f(x) |² dx Hint: Recall the Cauchy-Schwarz…

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Q: 5. If f is continuously differentiable on (0, 1] and f(1) = f (0) = -1/6, prove that dr 22 2 Hint:…

A: Continuously Differentiable Function: A function f is continuously differentiable on [0, 1] if its…

Q: f:(-m,m)-R, f(x)=xt cosx, (MER") function, at the point of a t (-M,m) COSX Ts this function uniform…

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Q: Using the e, d definition of uniform continuity: Prove that f(x) = x² is not uniformly continuous on…

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Q: 1. Assume f(r) is a twice continuously differentiable function on the closed interval (a, b), which…

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

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

Q: (a) Let g(x) = x3, and classify each of the following as positive, negative, or zero.

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Q: A function f of x and y is harmonic if a?flôx² + ??f/ôy² = 0. Prove that the functions defined in…

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Q: decide if the given statement is true or false,and give a brief justification for your answer.If…

A: f and g are integrable functions such that f(x-3)=g(x).

Q: 3. At which points of R? is each function continuous? Explain your reasoning. (a) f(x, y) = cos(xy+…

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Q: 2x +2x² + 3x² +3y² x²+y? a) Let f(x, y) ={ if (x, y) # (0, 0) Find the value of b for b if (x, y) =…

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Q: (a) Show that f(x) = x° is a ,3 contraction on X = (0, 5), but it has no fixed point in X. Does this…

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Q: 5 - x, -1 sx 2 r - 1, 2 <xs 3 Discuss the continuity of g(x) = %3D

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Q: ose ƒ : [a,b] → R is an increasing function, meaning that c, d = [a,b] with d implies f(c) ≤ f(d).…

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Q: x² + y³ x² + y? if (x, y) 7 (0,0) Define the function g: R² → R by g(x, y) if (x, y) = (0,0) Show…

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Q: please answer thank you!

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Q: f: R R be a continuous function and 3 (f(2x + ry))-f(x-ry) s1 nelvx, ye R, Ir-1 prove that f(x) is…

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Q: Q1. Let f: R² → R be defined by x3 + y3 r² + y² if (x, y) # (0,0) if (x, y) = (0,0). f (x, y) = (a)…

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Q: Example Prove that sin(xy?) x2 + y? ' 0, if (x, y) # (0, 0), f(x, y) = if (x, y) = (0,0) is…

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Q: Fundamental Theorem: 2x sin t -dt. Find the value of f'(x). t2 +1 Let f(x) = | %3D

A: We can solve this as follows:

Q: 3. Let f : R→ R be continuous and let a > 0. Define g : R → R by rx+a g(x) = f(t)dt, x € R. x-a Show…

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Q: 5. Knowing that the functionf:R R, defined by f(r) = sin z has 0 as a fixed point the a contraction…

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Q: V4 - a2 Given f(x) and g(x) = |x|, fogis continuous on the interval %3D 이-2,-1] U [1,2] o[-2, 1) U…

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Q: f: R → R be a continuous function and 3' (f(2x+ry))-f(x-ry) s1 nex,y E R, r-1 prove that f(x) is…

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Q: 1-cosx , x*0 is continuous at x=0 Find k so that (x) =; 4x2 Ik, x=0 A 1/2 в) 1/8 (с) 3/4 D) 2/5

A: Use the definition of continuity to solve a given problem.

Q: 8- Z,[x] is an integral domain. a) True b) False

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Q: following function show that the @f(z)=3z²+57-6 f(2)=4e²+ sinz b are analytic

A: Above question is solved.

Q: Is the function h(u, v) = cos(u) + e™u + sinh(u²) + vv+ eu , Where n is second digit of your arid…

A: Use the properties that a term inside the square is supposed to no-negative number to get real…

Q: Q1:Discussion a continuity of the function f(x, y) at the point (0,0), where rey sinx (x, y) = (0,0)…

A: Given that fx, y = ey sin xx , x, y ≠ 0, 01               , x, y = 0, 0 . We have to discuss the…

Q: 64. Continuous extension Define f(0, 0) in a way that extends x² - y? f(x, y) = xy x² + y? to be…

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Q: 4.6 Lemma Let a be a curve in R' and let f be a differentiable function on R'. Then d(f(@)) a'(S] =…

A: We will apply the extended Chain Rule of differentiation to prove the given Lemma.

Q: Q2/ let f (x) x2-4x +7, then f is continuous on [0,4] and differentiable on (0,4) find the value ce…

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Q: cs) Show the function is continuous at r = 0 by using de nods receive zero points, for example,…

A: The value of sinx varies between -1 and 1. L.H.S limx→0- x4sin1x=limx→0- x4 . [-1,1]…

Q: Ono. 6b) Proue Trut if f integrable [o,1, Hen on ei S znfcandx

A: Here f is integrable on [0,1] then we have to prove that limn→∞∫01xnfxdx=0

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: (-x^2, x < a Vx, x z a Find the value of a such that f (x) = f(x) = is continuous everywhere.

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Q: QI If f(2) s analy tic function for all 2 Prove tha t dy

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Q: find (Ix - xl) vx€ (-1,1) and x # 0. dx (b) Test the continuity of the function f(x) = sgn(lxl) at x…

A: Answer

Q: Q2/ let f(x) = x2-4x + 7, then f is continuous on [0,4] and differentiable on (0,4) find the value…

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Q: Q2) show that the function f is continuous at the given point 23 – 1 |z| # 1 1+iv3 z2 + z +1 -1+iV3…

A: In order to answer this question you have to know the following notion:

Q: 6x2 - x2y +6y2 Define f(0, 0) in a way that extends f(x, y) = to be continuous at the origin. x2 +…

A: The function fx,y=6x2-x2y+6y2x2+y2 is continuous at the origin.

Q: Ol a fundtion f is nt defined at X =a Then it is not continuQus at z= q

A: Given,          A function f is not defined at x=a.

Q: The function f : (,,0) → R given by f(x) = it is not uniformly continuous on (;, 0). 1 is continuous…

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Q: f(x) = jx+2 f [o,4) - IR Is it continuons? uniformlu contiauous HWI s? egui.continuous?

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: 1-x², x 2 at x = 2.

A: Given, fx=1-12x2, x&lt;23,    x=2x-2-1,   x&gt;2

Q: (b) Is the function h(u, v) = cos(u) + enu +sinh(u?) + vv+ enu , Where n is n=8. Is h is continuous?…

A: