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 constant.

Q: (a) Assume that g(x, y) is a function of the form x²+y² g(x, y) = 0 if (x, y) = (0,0). (i) Show that…

A: (a) The given function is gx,y=x3yx2+y2  if x,y≠0,00             if x,y=0,0. To show: (i) gx,y≤xy…

Q: xy Prove that the function f(x, y) is differentiable everywhere in its do- x² + y? main.

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Q: f(x) is a positive continuous function on R what does the function F(x)= | f(t) dt a represent (for…

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Q: z sin (), if (2, y) # (0, 0) 2. Determine if a function f : R2 → R defined by f (x, y) = %3D 0, if…

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Q: f(x, y) = 3x² - y x4 x² + 2y ² 1 (x, y) = (0,0) 2 D (X,Y)= (0,0) 1 Determine if f is continuous at…

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Q: Isin , it (z, y) # (0, 0) 2. Determine if a function f : R → R defined by f (r, y) = 0, if (z, y) =…

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Q: f(z) is a twice differentiable function with f(0) = 1, f(2) = 4, f'(2) = 5, Then af"(x)dx = %3D

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Q: { z sin a). if (x, y) # (0,0) 2. Determine if a function f: R2 R defined by (. 9) = BE 0, if (KJ) =…

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Q: (b) A continuous function f : [0, 1] → R such that its graph (r, f (x)) C R² is not closed.

A: The given statement, "A continuous function f:0,1→R such that its graph x,fx⊂R2 is not closed" is…

Q: Let f:XT, → XT, such that f({a}) = {b, c} į Is fa continuous function? i yes,no, or can't you tell?…

A: Let (X, ΤX) and (Y, ΤY)be topological spaces A function f : (X, ΤX) → (Y, ΤY) is continuous  if…

Q: ; (xy) (0,0) x +y -- Investigate the continuity of f(x, y) %3D ; (xy) = (0,0)

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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: Let f : R² → R with f(x,y) = x²+ y. Prove that f is differentiable at the point (0, 0)

A: Given function is f(x,y)=x2+y Since we know that, differentiability of function of two variable at…

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: Q4:- Exam the limit of f(x,y) (xy) (0,0) as (xy)(0,0) along the line y = mx, and along the parabola…

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Q: a²+y² » (x, y) # (0, 0) f(x, y) : 0, (х, у) — (0,0).

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Q: (a) Assume that g(x, y) is a function of the form g(x, y) = {" 0 if (x, y) = (0,0). (i) Show that…

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Q: Exercise 8 x²y if (x, y) # (0,0) The function f(x, y) = } x²+y² if (x,y) = (0,0) is not continuous…

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Q: x+y if (x, y) # (0,0) (1 if (x,y) (0,0) Q.3 ( 3+3+4) (a) Prove that the function f(x, y) is not…

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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: a sin (), it (, u) + (0, 0) x²+y? 2. Determine if a function f : R² → R defined by f (x, y) = 0, if…

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Q: Determine if the function √x² + y² +1 x² + y² f(x, y): 1 2 is continuous at (x, y) = (0,0). If not,…

A: To find whether the given function is continuous or not at(0,0).

Q: f : R → R be defined by f(x) = x² + x. Pro nition, that f(x) is continuous at all a E R.

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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: # Determine whether the function z = f(x, y) = { (why or why not) for for (x, y) = (0,0) (x, y) =…

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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: I. Show that the function f defined by 1, (x, y) = (1, –1) %3D f(r, y) = { r2 + y (x, y) + (1, –1)…

A: Given function is  fx,y=1,             x,y=1,-1x2+yx+y,    x,y≠1,-1

Q: Let X 2 0 be continuous. Show that E[X] = So° (1 – F(x)) dx.E[X] = S,° (1 – F(x)) dx. %3D

A: Let X be a continuous variable lies in interval [-∞,∞] with its probability density function f(x).…

Q: xY (a) Prove that the function f(x,y) is differentiable everywhere in its do- x² + y? main.

A: Differentiablility: A function z=f(x, y) is said to be differentiable in its domain D if the partial…

Q: I sin () if (r, y) # (0,0) 2. Determine if a function f : R2 R defined by f (x, y) = 0, if (r, y) =…

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Q: 3x²y f(x, y) = {x + y² if (x, y) = (0, 0) if (x. y) = (0, 0) %3! norn (r u) uma f.

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Q: At what points (x,y,z) in space are the functions continuous? a. h(x,y,z) = In (5z° - x-y² - 3) 1 b.…

A: In this problem, we have to check condition for having the function continuous.

Q: (d) The function x²+y? Vx2+y? (x, y) # (0,0) f(x, y) (x, y) = (0,0) is continuous at (0,0).

A: Note: according to Bartleby policy we are allowed to write only one question please post remaining…

Q: I. Show that the function f defined by 1, (x, y) = (1, –1) f(x, y) = { x2 + y (x, y) # (1, –1) x + y…

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Q: Discuss the continuity of the function. f(x, y, z) = xy sin z

A: Given- fx,y,z=xysinz To Discuss- The continuity of the above function. Concept Used- A function is…

Q: e-(z-1)2-y 1 (r, y) # (1,0) If f(r, y) = (I-1)2+y (r, y) = (1,0) %3D is continuous at (1,0), what is…

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Q: Let f(r, y) 3ry? when (x, y) + (0,0) and f(0,0) = 0. g²+2y! At which points is f continuous?

A: The given function is: This function is continuous at a point if at that point limit exists and the…

Q: Find div F if F(x, y, z) = (x² + y)i + z²j + (eY - z) k.

A: Our Aim is to find the value of div F if F(x,y,z)=x2+y i +z2 j+ey-zk -(i)Let  F(x,y,z)=x2+y i +z2…

Q: # Determine whether the function z = f(x, y) = (why or why not) for for (x, y) = (0,0) (x, y) =…

A: Given the function z=f(x,y)=x4+y4x2+y2 for x,y≠0,01             for x,y=0,0. The objective is to…

Q: (a) Assume that g(x, y) is a function of the form 2+y² g(x, y) = 0 if (x, y) = (0,0). (i) Show that…

A: As per our guidelines we are supposed to answer only first question's first 3 subpart. In this case…

Q: Determine if the function f (x, y) = if (x, y) = (0,0) is continuous at (x, y) = (0,0). If not,…

A: Use limit to find wheather function is continuous or discontinuous.

Q: At what points (x, y, z) in space are the functions continuous?  a. h(x, y, z) = sqrt(4 - x2 - y2 -…

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Q: (d) The function x²+y? Vx²+y? (x, y) ± (0,0) f(x, y) = (x, y) = (0,0) is continuous at (0,0).

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

Q: Show that the function f defined by (x, y) = (1, – 1) f(x, y) = 1² + y (x, y) # (1, –1) I + Y is not…

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Q: (a) Assume that f(r, y) is a function given by ry if (x, y) # (0,0), f(r, y) = if (x, y) = (0,0).…

A: We  need to prove the continuity of the function at (0,0).

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

A: The given function is- fx,y=lnx2y-x Partially differentiating it w.r.t. x- ∂f∂x=2xy-1x2y-x Again…

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.