Q/ if f continuous map Prove that f(B) = f(B), VBCY

Q: Let In, f be real fun ction on 52.Show {w : fu(w) yo frw) }=Ŭ o U {w-1fu(w) %3D f(w)1>と3

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Q: Local linearization is used to justify L'Hopital's Rule when f and g are differentiable and…

A: Not only zero , when both f(a) and g(a) are infinite , in that case we can also use L'Hospital rule

Q: Find | of ax 11 of and ay for the function f(x,y). f(x,y) = g(t)dt (g continuous for all t) X

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Q: Consider the function a) b) Prove function & R R given by Prove there that Prove f'(e) f(x) there…

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Q: Q3-A) Is the function F(Z) continuous or not at z-U? 1+|21,

A: Let z = x+iy then Re(z) = x and |z| = √(x^2 + y^2) If z = 0 => x = 0 and y = 0

Q: Prove there does not exist a continuous function which maps the closed interval [0, 1] onto the open…

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Q: Consider the following statement: There do not exist 2 × 2 matrices E, F with rank(E)=rank(F)= 2…

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Q: 1 is IR? \ {(0,0)}. 22 + y2 The domain of the function f(*, y) True O False

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Q: [2х 81 2) For what values of (x) does the matrix : 1 a)singular b) non-singular

A: Given matrix is  A=2x81x Now,  A=2x81x=2x2-8=2x2-4 So, A is singular when A=0 which occurs when x2-4…

Q: Let /: X →Y be a function, A, BC X and C, DCY. Show that: 1. f(AUB) = f(A) uf(B) 2. If AC B, then…

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Q: The function f(x, y) = ¿e=y – In(y²)

A: It is partial derivative

Q: f(x,y) F(x,y)= (x,y)+ (0,0) (x,y)= (0,0)

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Q: (4xy) w = 3 sin (4xy tan (z) +4 In (5yz)- 8 e

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Q: Let f(x, y) : = x/Y Evaluate f(3, 4)

A: We need to evaluate f(3,4) To evaluate we need to plug in 3 for x  and 4 for y

Q: Write down the first order and second order conditions for maximum and minimum of a function y =…

A: Given,  Function y = f(x1, x2, x3,  .  .  .  , xn). To find the first order and second order…

Q: Q/ if f contineous map Prove that f(B) ≤ f(B), VBsy

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Q: A function F is defined on R² By: f (x, y) (x, y)# (0,0) F (x, y) = (x, y) = (0,0) y+2xy² x²+y2 Let…

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Q: Using the - definition of continuity, show that the func- tion f R³ R² defined as f(x, y, z) = xyî +…

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Q: Let F cos(5t) i + 3tj+ 5t° k and G = cos(5t) i + t j+ 5et k

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Q: Mathmatic Let f : ℝ2 → ℝ be a continuous function, and let S be the subset of the ℝ2 given by all…

A: Given that f:ℝ2→ℝ be a continuous function, and let S be the subset of ℝ2 given by all pairs x, y so…

Q: Let f(x,y,z,w)=45x3z-1/y+wz3. Evaluate f(a,b,c,d) where a,b,c are non-zerol real numbers

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