3.2 † Prove part (ii) of Theorem 3.1.2. Theorem 3.1.2 Let f and g be in R[a, 6} and c e R. Then i. f+g€ R[a, b) and (f + g)(x) dx = f(x) dr + | 9(x) dr. ii. cf e Rla, b] and | ef(2) dz = c f(2) dzr.

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A: Use Hessian matrix

Q: Find the functionr that satisfies the following conditions. r'(t) = (5t*,1,41); r(1) = (- 5,7, - 9)…

A:

Q: 4. Find two possible non-linear functions & and such that goh= √sinx-x²

A: To find the non linear function by the given composition.

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A:

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A:

Q: Given f(x, y) = 50x + 70y − 5x² − 3y² – xy, and evaluate ƒ(10, 7). f(10, 7) =

A: To evaluate f(10,7)

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A: For the function f( x, y, z ) = x2y + y2 + xz2 . We need to find some partial derivatives.

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

A:

Q: 10.2 Evaluate f(0,1) f(2) dz when f(z) is (i), (ii) (Rez)², (iii) z-2 (4-1), (iv) sin z. (Use the…

A: To find : ∫γ(0;1)fzdz when  (i) z4 (ii) Re z2 (iii) z-2z4-1 (iv) sinz

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A: From the graph of the given distribution function it is clear that we can say the Y is related as…

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A:

Q: Find all the numbers for which f(x)20 if ƒ(x)= x* +2.x² +x² – 2x – 2. a. x>1. b. 지2-1. c. -1<x<1. d.…

A: First, draw the graph of f(x)=x4+2x3+x2-2x-2 . If the graph of f(x) is above the X-axis for the…

Q: Let f(r) = In r Find and simplify f"(x).

A: Please refer the attached image for complete solution. THANK YOU.

Q: Consider the function f(x): = 5x³ - 7. 20 4 a. Over what interval(s) is f concave up? (If f is never…

A: fx=320x5-34x4-5x3-7

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A:

Q: 2. Compute L4, R₁ and T₁ for the function f(x) = 2 on interval [1, 2]. Verify result from question…

A:

Q: Describe the domain of the function f(x, y)= In(6+x-y). {(x, y): y<x-6} {(x, y): y 2 0} a. {(x, y):…

A:

Q: You are given that · z+5y. In(x) - x6 +5= 0. - Here x is a function of independent variables y and…

A:

Q: QUESTION 6 Consider the function f(r, y, z) = 6x² + 4xy+ e4yz af Then is equal to: ду O A. 4x +…

A: we find out partial derivative with respect to y.   see 2nd step.

Q: 3. Let f(x, y) = (2x – y,x- 2y); (x, y) E R x R, (R is set of real numbers.) a) Show that f is one…

A:

Q: Determine the length of x = 3+ (y – 2)², 4<x< 19

A:

Q: 4. Let function f: R → R and function g: R → R be two functions for which f(g(x)) = x and g(f(x)) =…

A: We have to prove given statement.

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A:

Q: Which function is best represented by the graph to the right? 8 A y=-2x +3 -4 B y=-2x + 6 9-8-7 -1…

A:

Q: Any function of the form f(x, y) = ax*y" where a is a real number and k, n are positive integers…

A:

Q: 10. Let F(x, y, z)= y-yz+1 £z+r-z z+xy-y Find a function g such that F = √g.

A:

Q: Determine a potential function to evaluate (F*dR for C any path from the first point to the second.…

A: Given:F=3x2(y2−4y)i^+(2x3y−4x3)j^​Two points: (x1, y1) = (-1, 1)(x2, y2) = (2, 3)To determine a…

Q: Inverse Functions beduined Let f: R→ R be defined by f(x) = 3x +2. Show that f is bijective and find…

A:

Q: 6. Let f be function such that f(-a) = - f(2) for all If a %3D х. | f(2)dz = 5, then L2) +0)dz =…

A: With the help of definite integral property we solve this.

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

A:

Q: 1. Considering the following graph of f(x). -2 2 6 i. Circle the interval(s) where f '(x) is…

A:

Q: 2. (8.7.10) Let f (x, y) In y R is the rectangle defined by R {(x, y)|1 < x < e2 and 1 < y < e}.…

A:

Q: Let f (x) = vr +2² + 2 , ro = 1, h = 0.5, r1 using the Three-Point formulas to approximate f(1) (1);…

A: Given: The given fx=x3+x2+2, x0=1,h=0.5,x1=1.5 and x2=2

Q: 3. Let f A B be a function, and let Ao C A, BoC B. Prove that (a) f(f(f(Ao))) = f(Ao); (b)…

A:

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

A:

Q: 8. Consider the functions f : (4, 0) → R where f(x) = sin x and g : (-12,3) → R where g(x) = |x +…

A: Solution

Q: Determine f„ (0, T, 1), fy(0, , 1), f¿(0, r, 1) given the function z sin(3xz+ y²)

A: The given function,        zsin3xz+y2