b₁ + x b₂ + x b3 + x + +x\ C₂+x, then show that A'(x) = 0 a₁ + x If A(x) = a₂ + x a3 + x C3 + x and that A(x) = A(0) + Sx, where S denotes the sum of all the cofactors of all the elements in A(0).

Q: Cansider h(x)= Ilx? -6x = l|x? calculate Ha) 6 .x T1 3 (22r – 6) A) In(3)- 11 (22.r – 6)3** - (11z²…

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Q: sin(32) Let f(z) and C: |z| = 1. Then ſ. ƒ(z)dz = %3D (1-2);z а. О b. Злі c. -6ni d. None of the…

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Q: 4. Perform the indicated multiplication of the two differential operators: (D –x)(x²D– 2x).

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Q: A X(t) = [² 2x+ JUC) Find A-¹ by the Cayley-Hamilton Theorem X26) = (-₁ [SI-A)-¹(x (0) Find X(2) if…

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Q: Find all. (xo, Yo) in which f(x,y), y(x) =Yo has a solution and a unique solution on some open…

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Q: What is the linear approximation of this function at (1,0) F(x, y) = (F(x, y) = (x² cos(x+y)) x²y 0…

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Q: Let g(s) = (282)7. Then g'(s) is g'(2) is g" (s) is and g' (2) is "

A: Solving the following problem

Q: Derive that (x + y)(x' + z)(y + z) = (x + y)(x' + z) by using boolean algebra.

A: Kindly go through the solution and let me know in case of any doubt or further clarification in the…

Q: Let 7'(t) = (3+ 4t, cos(t), 6e*) and F(0) = (7, 2, 5). Determine 7(t). †(t) = (, , )

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Q: Find the residues of the followings functions at z = 0: (1) (z² + 1)/z (2) (z² + 3z – 5)/2³ (3) (2z…

A: 3. Given function is 2z+1zz3-5.

Q: The Domain of f (x) = V1 – x is 1. [-1, 0) 2. (-∞, 1] 3. (-0, 1) 4. [1, c0)

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Q: Suppose z = x + iy and f(z) = z - 1. Find w = u + iv such that f(w) = 1 + 3i (A) 3+2i (B) 3-2i (C)…

A: We have given that , fz = z - 1 , where , z = x + iy Here , w = u + iv Let , fw = 1 + 3i We need to…

Q: 1 1 T+ 2 1 B T+ - T(2)"-1 3(T, T)

A: To prove  βT+12,T+12=πT24T-11βT,T It is known that  βm,n=ΓmΓnΓm+n Now, for m=n=T+12,…

Q: 8 Describe the long run behavior of f(x) = x° – 5x* + 5æ° – 1 - - As x → - 0o, f(x) → ? As x → 0,…

A: Given  f(x) = x8-5x4+5x3-1 We have to find the end behavior of the function.

Q: Stan"( 1 -tan m+2 -tan m+1 m+1 1 m+3 Evaluate A B Ⓒ D tan" (x) sec¹x dx. (m + -2)(x) + ¹) (x) - 1)…

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Q: Let p(x) =-2x* + c,x' + c,x + c,x + c, x ER be a polynomium whose graph insersects the points (-2,…

A: Given. We are given a fourth degree polynomial and also four points on the curve of the polynomial…

Q: Determine whether the given set of functions is linearly independent on the interval (-co, co).…

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Q: The function y = (x- 1)(x-2)(x - 3) is negative on the interval(s) %3D O a) xe (-0, 1) and x e (2,…

A: We have y=x-1x-2x-3 First, we find the critical points by letting y=0: y=0⇒x-1x-2x-3=0⇒x-1=0, x-2=0,…

Q: Let C be a constant. Consider Compute(a) da. ان | دن 3 7 3 73 ㅠ + CT 53 + СT 7 + СT 3 -x², f(x) 2) =…

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Q: 1 1 (sin ßt – Bt cos ßt) 283 (s2 1 -sin ßt 2B

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Q: Let Var(X₁) = Var(X3) = 2, Var(X₂) = 3, Cov(X₁, X₂) = 2, Cov(X2, X3) -2, Cov(X1, X3) = -1. i)…

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Q: f(x,y) = –x² + 2xy + 3y² – 6x – 2y – 4 | - Serialize the function around the point (-2,1). a) f(x,y)…

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Q: 5. If f (x) = (x + 1)(x2 – 2)3 then f'(x) da व्य 2= 2x (1) 2 A. & 6xx2 – 2)2 انی + (22 21 2 = Alv 3x…

A: Given query is to find the derivative of the function.

Q: Let a(t), 2 < t< 8 be a positive function. Also, let the function 8(t) be defined as a'(t)/a(t) on…

A: We will find out the required expression.

Q: Let g(x) = 2 f(u) + 3 where . u= u = with respect to x? ○ 2. f' (u) +3 O (2. f' (u) + 3) (2x + 2)…

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Q: Given that f(x) = 2x + cos(x) is a bijective function, find (f-')'(1)

A: The function f-1 represents the inverse of function f. Therefore, if f-1x=y then x=fy represents the…

Q: waluate Stan" (x) sec¹x de m 1 m+3 −tan (m+3)(x) + 1 m+2 1 m+1 1 m+1 1 m+1 tan n (m+2)(x) + — tan”…

A: We will evaluate the given integral as shown below

Q: Find the residues of the followings functions at z = 0: (1) (z² + 1)/z (2) (2² + 3z – 5)/z3 (3) (2z…

A:

Q: Consider the following bijections on R: f (x) = - g(x) = x – 7 Then (f o g)¯'(x) =

A: Given, fx=-x,gx=x-7 Find the value of f∘g-1x.

Q: If the invertible function f (x) satisfies f (12) = 6, then which of the following statements is…

A: Option C is correct option.