find the nUmbers b such that the auerage due of f(x)2+6x-3x on the interval E LO,b) is equel to 3

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Q: Explain why the Intermediate Value Theorem is not necess arily guaranteed fo f (x) = = CSC for x E…

A: Topic = Functions   The intermediate value theorem states that if f is a continuous function whose…

Q: Consider the function y = 5cos(x). What are the exact values of C in the interval [0, 2pi] such that…

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Q: : Apply Rolle's theorem for the function f(z) = 7x² – 28z+ 21 over the interval [1,3]. er.

A: The given function is, f(x)=7x2-28x+21 over the interval [1,3]. Observe that, the given function…

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Q: The function f (x, y) = sin(xy)/xy is defined for xy ≠ 0.(a) Is it possible to extend the domain of…

A: conditions of function to be continuous: At each joining point the value of limit from both sides…

Q: Consider the function F(x, y) = x + 3x2 - 6xy? +2y3, Find critical points (FoC). Identify these…

A: Given function  F(x,y)=x3+3x2-6xy2+2y3 a. Differentiating F partially w.r.t to x and y, we get…

Q: what is the quadratic polynomial for the function f(x,y) sin(xy) + cos(x/y) at (pie/4, 1)

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Q: af Find a d () + In (). of the function f(x,y) = arccot and ду

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Q: Assuming - 6x° -y² + 7xy = 0 defines y as a differentiable function of x, use the theorem Fx to find…

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Q: 4. Integrate the function f(z) = z² + 2z from z = -i to z = 1 in two ways, once along a straight…

A: The objective is to integrate the function fz=z¯2+2z from z=-i to z=1 in two ways, Once along the…

Q: find the fun Ction Y= f(x) that satisfies hp Jメ 8x² + 7 , 7, F (0) = -13 コ

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Q: is concave up on interval The graph of f(x)= x2 – 1 OA(-1,1) OB (0,1) oC(-1.0) U (1, 00) OP (-x,-1)U…

A: F is concave up if f’’(x) > 0.

Q: of and dy For the function f(x,y) = In (8x + 9y), find - - of

A: partial derivative of two variable functions

Q: 2. k) Show that fe2) = function is analytic %3D t'+s for Rez 70.

A: Calculate the limit: lim∆z→0fz+∆z-fz∆z=lim∆z→0∫0∞e-tz+∆zt2+1dt-∫0∞e-tzt2+1dt∆z…

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A: We have to find fx , fy , fz.

Q: x - y -2x Prove by definition that for f(r, y) fy(x, y) = %3D x+ y' (x+ y)2

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Q: Please show step-by-step solution

A: Given function is Firstly, we will find f'(x) and f''(x)

Q: Use the limit definition to compute f' (a) and find an equation of the tangent line. f(t) = √(t2 +…

A: Consider the provided function, ft=t2+1    a=3 Find the limit by the definition to evaluate  f'a and…

Q: my (x, y) # (0,0) x2+y2 f (x, y) = (х, у) - (0,0)

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Q: faow that the function f depthed by (X .Y) = (1, - 1) f(XrY) = %3D x2 + 냉 (x, y) $ (1,-1) * ty is…

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Q: Find a point zo where the function f (z) = (z – 8 – 6i) (z – 8 – 6i) is differentiable. What is the…

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Q: to verify thiIS 1 For which values of a ER is the function ax? f(x + iy) = (ax- ary) + i + ay 2 an…

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Q: ,is concave up on interval x2-1 The graph of f(x)D OA (-1,1) OB. (0,1) В. Oc. (-1,0) U (1, 0) OD.…

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Q: The domain of f(x,y) = In xy is points (x, y) in the first quadrant Select one: O True O False

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Q: What is the absolute minimum value of f(x) = æ + sin a on the interval ,

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Q: 9. Show the function f(z) = 1 + 2i+2Re(z) is differentiable or not differentiable at any points.

A: Solution

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A: Given: xyx2+y20,x=0,x≠0 According to the given problem: At x=0. fx(x,y)=fy(x,y)=0

Q: The harmonic function for f(z) = u(x,y) + iv(x,y) to be analytic are:

A: Given that: f=u+iv

Q: Suppose f: a,b] → R is continuous and faf=/ for all xie [a,bl Show that f(x)= 0 ft rEla,b).

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Q: Use the limit definition to compute f 1 (a) and find an equation of the tangent line. f (t) = 2…

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Q: Q10. Expand f (x, y) = e" cosx about up to third degree terms by using Taylor's theorem for a…

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Q: 4. Determine the set of points at which the function is continuous. cos(xy) b) f(x,y) = e? – y? '

A: we have to determine the set of points at which the function is continuousgiven function,…

Q: et f(x)=x2 ,on interval 0<x<2n , sketch and find an älo glaj

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Q: The range of the finction f(x, y) = In(-x² -+1) is %3D None of these O (00:0] O [0; +0) O [0;1]

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Q: Given, f(x;x) = * – 2xy + 2y on the ractange o Find out the absolute minimum and Maximum values foro…

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Q: Calculate the approximation of My for the given function and interval f Cx)=フメーンLュ,3 %3D

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Q: Along the straight line x + y = 1, the function f(x,y) = xy has a local extremum at the point (0,0)…

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Q: Show that the function f(x, y) xy? – 1 has y – 1 no limit as (r, y) → (1, 1).

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Q: ar +b. 2r' - 1, f(z) = I>3

A: The given function,fx=ax+b,x≤32x-1,x&gt;3

Q: Suppose f(z) = (z – i)³e² is analytic inside and on circle |z – i| = 3. Then the upper bound of…

A: Given that f(z)=(z-i)3ez- is analytic inside and on the circle|z-i|=3To find the upper bound of…

Q: The range of the finction f(x, y) = In(-x2-+1) is %3D None of these O (-00:0] O [0; +0) O [0;1]

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Q: (a) Use the Product Rule twice to prove that if f, g, and h aredifferentiable, then (fgh) '= f'gh +…

A: (a) Given: Since f,g,h are differentiable functionsLet us consider the two product functions as u(x)…

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A: Here we have to find fx , fy and fz  of

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Q: y y =x – x12 1 Rogawski et al., Calculus: Early Transcendentals, 4e, © 2019 W. H. Freeman and…

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Q: Find a function f:R² → R, its tangent plane at the point (1; 1; f(1; 1)) is given by -2x – 9y – z+8…

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