Let f : R" → R be a function. Consider the converse proposition of (6.1) given below: If La(f) is a convex set for each a E R, then f is a one-to-one function.

Q: Find the value of c that satisfies the MVT of f(x) = 1+x + x2 on (0,2).

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A: Given: f(a)n=1 if n=0nan-1 if n≠0and f(b)n=bn To find: b2010=?

Q: Prove that •1 to(xt) 1-1² dt = Sinx x

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Q: f (t) = 3e" cosh (In 2r -2t

A: Given,                 f(t)=3e-2tcoshln2t

Q: L{f(t – a)u(t – a)} = e¬as F(s) |

A: Topic:- Laplace transform and it's properties

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Q: R defined by f(x, y) = 2x³-12x² - 6xy+3y² +24y. Consider the function f: R²- a) Find the Cartesian…

A: If a real function of two variables  is differentiable whose second partial derivatives exists and…

Q: Integrate: +C 16t6 t4 [√16 dt

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Q: -22°y+3ry3 (a, y) # 0 0, (x, y) = 0. ||

A: Given,       f(x, y)=-2x3y+3xy3x2+y2,x, y≠0, 00,(x, y)=0, 0

Q: Expand [× (à × ř)] d dt

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Q: H 2= x? tan y/ at (lo1) %3D Ex by

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Q: Show human working please

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Q: Aagamant # os Q#os Find he harploce truriJerm og the Jenetim EBinut 26 Ginan that 7(2125) = 7(t)

A: Laplace transform of periodic function: The Laplace transform of a periodic function f(t) of period…

Q: Q2: Expand f(x,y) = [sin (x y³)]² about (5, 1).

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Q: dt 1). S V16-9t2

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Q: firm has the Cobb-Douglas production function y = is using the input bundle (27, 16, 64). O How much…

A: The Cobb-Douglas production function y=10x113x212x316. The input bundle is 27, 16, 64

Q: xy If z show that: x- y

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Q: Show that f (x) = 1 − |x| satisfies the conclusion of the MVT on [a, b] if both a and b are positive…

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Q: やx) - 3-X 2: To fmel つ Let 3-x>。

A: We have to find the domain of the given function.

Q: +x 5) Let z = f(x² – y²). Show that y ду əx az

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Q: x+3-2 f(x) = f'(1)? x+2

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Q: Show that f(z) = Re(z) = x is not differentiable at any z. W 20

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Q: = Let y 2x2 linear approximation + 7x + 4. If Ax = 0.1 at x = to estimate Ay 2, use

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Q: Use reiation Ship: the fcx) (x) To Calculate Js?

A: Here, we need to calculate √8. In other words, we need to find the root of the function f(x) = x2 -…

Q: Verify that (AB)" = BT AT %3D التحق ق 3 2 4 2 1 3 A = 2 1 B =1 2 5 4 2 3 0 2 1

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Q: Suppose that f: [1,9] →→ R² such that f(1) =(2,-2) and f' (t) Find f(9) (v₁, 71) √t, √t

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Q: Let f(x, y) = √150 – 4x² – 2y² Evaluate f(1, 1) vad

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Q: Consider f(x, y) = x³ + 2ry + y. Compute the following: (b)

A: Answer and explanation is given below.. Simply do partial derivative with respect to x and y.

Q: For æ > 0, 1 dt 1+t2 A 2/7(1+z) B 2/7(1+JE) c) 1+1 D 1+z E VE

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Q: Compute f, for f(x,y)=xln(xy). %3D

A: We can find the answers as below.

Q: Let f(r) = Vt3 +1 dt for r2 3. 3

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Q: Given f(x, y) = 9xy® – 6x*y. Compute: a?f ду? ||

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