5. Let f, and f, be the function from R to R such that f,(x) = x²+2x+3 and f,(x) = x-x. What are the functions f,+f, and f,f,?

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: Suppose that f: [0,1]–R is a function satisfying the conclusions of the intermediate value theorem.…

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Q: Suppose that F(x, y, z) = 0 defines z as a function of x and y and F is differentiable. Prove that…

A: Solution is given below:

Q: 3. Compute the value of F.dr if F = -yi + xj and C is a semicircle from (-1,1) to (1,-1).

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Q: The set of all points where the function f(x) = x |x| is differentiable is (A) (-∞, ∞) (B) (-∞, 0) U…

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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: of and ду of For the function f(x,y) = In (x+ 3y), find

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Q: 6. Give four non-trivial functions f(x), g(x), h(x) and j(x) such that Vx2 – 1+5 - (f ogohoj)(x) = V…

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Q: f(ix, λγ) - λκ. f(x, y)

A: Given: fλx,λy=λkfx,y

Q: 1 If f(x,y,z)= of then x-y-3-

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Q: 18. Suppose that f is a differentiable function such that f(g(x)) = x, and f'(x) = 1 1+(f(x))². Show…

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Q: Let f:R→R be defined by f(x) : [ 2x – 1, z<2 | 2x +1, 22 , then f-'(4, 7() is None of the choices O…

A: Hello. Since your question has multiple parts, we will solve the first part for you. If you want…

Q: Suppose that f(x, y) = yvx* + 1 on the domain D = {(x, y) | 0 < y < x < 5}.

A:

Q: (5) Find the most general function f(t) so that the curve F(t) =, shall lie in a plane.

A: The most general function for f(t) is a constant function, f(t) = c:   &lt;a cost, a sint, c&gt;

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: 4. Verify Rolle's Theorem for f(x) = x² – 2x +1 on [-1,3]

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Q: 4. Verify Rolle's Theorem for f(x) = x² – 2x + 1 on [-1,3]

A: Verify Rolle's theorem

Q: Show that if f (x, y, z) = 0 then = -1.

A:

Q: 1. Find of ахду OF f(x,y) = xy (x+y-1) -x2

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Q: +1 Differentiate the function f (x) = In +1

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Q: Suppose that the function f: [0, 1]  in R is continuous and thatf (x)&gt;= 2     if 0 &lt;= x &lt;…

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Q: The graph of f(x)= x2 - 1 is concave down on interval | (-1,1) ^O (0,1) BO (-1,0) U (1, ∞ )co (- 00…

A: From the given problem:   fx=xx2-1   As we know that for concave downward:   f''x&lt;0   So,…

Q: If f is a function defined from R to R, is given by f(x) = 5x - 3 then f -(x) is given by %3D -- 20…

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Q: of of and ду For the function f(x,y) = In (7x + 9y), find

A: The given function,     f(x,y)=ln7x+9y

Q: Suppose that f(1)=8, f(4)=−4, f′(1)=−3, f′(4)=2, and f′′ is continuous. Find the value of ∫from 1 to…

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Q: Let † : R² → R be the function x2 if (x, y) + (0,0) f (x, y) = x + Y if (x, y) (0,0) By using the…

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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 is…

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Q: show that F(X<1|Y<y) + P(X <1) for some z, y.

A: dependent events:  Two or more events are said to be dependent if occurrence of one affects the…

Q: 8 Examine holomorphism of given function  f(z) = |z|2

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Q: Suppose that u(x) is a differentiable function such that

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Q: 5. Show that the function h(x, y) defined by 1 if a? + y? 1 is discontinuous.

A: We can solve this using R.H.L ≠ R.H.L

Q: Suppose that f(x,y,z)=x^2yz−xyz^3 is a function of three variables.

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Q: Let f(x, y, λ) = xy + λ(5 - x - y). Find f(1, 2, 3).

A: Given : fx,y,λ = xy + λ5 -x -y

Q: 7. Show that the function f : R → R* defined by f(x) is not onto. x2 +1

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

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Q: 5 Show that the function h(r, y) defined by if r +y? < 1 h(x, y) 0; if r +y 2 1 is discontinuous.

A: For continuity of 2 variable function L.H.L=R.H.L=Function value at (x,y). limx→a+,y→b+…

Q: Show that a function f : R2-R defined by f(x,y)= x3- y3 / x2+ y2, if (x,y) is not equal to (0,0)…

A: What is Continuous Function: A function is referred to be continuous at a certain point in its…

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: Differentiate the function.

A: Given function -f(u) = lnu1+ln(2u)Differentiating with respect to u - f'(u) = ddulnu1+ln2uf'(u) =…

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

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Q: Suppose f is a bounded real function on [a, b), and f' eR on [a, b). Does it follow that fe R? Does…

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Q: 4|x| – 3 pour x 1, x² – 4 f2(x) + V2 + x², || ||

A: Given that, f1x=4x-3x≤1-3xx2-4x&gt;1f2x=1+2+x2 To determine set of points which they are derivable…

Q: 1. Show (in terms of -5) that a function f: [2, 7] R be defined by f(r) V+1 is uniformly continuous.

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Q: 2. Consider the function f(x) = if x = {9 in lowest terms q > 0, p,q e Q; 0 if x e Q°,x = 0…

A: We use sequential approach of continuity to show it.

Q: Let S(x²+2x)², x> 1, f(x) = Tax+ bx², ах x< 1. Compute for all a and b such that the function f(x)…

A: Proceed as shown

Q: Suppose that a function f(x, y) satisfies fxx fyy – (fxy)² > 0 at a point (a, b). How is the sign of…

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Q: 5) Suppose a path C is defined by r(t), 2 and r(8) = . If f is a differentiable function satisfying…

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Q: 3. Let # 0, 0, r = 0. f(x, y) = Find f.(x, y), fy(x, y) at all points. Leave your answer as a…

A: We need to find differentiation of f(x,y) with respect to x and y.

Q: what sets X and Y is the function X Y defined by 3x f (x) = x +4 %3D ijection?

A: