4|x| – 3 pour x < 1 fi (x) -3x pour x > 1, x² – 4 f2(x) + V2 + x², || ||

Q: The graph of f(x)= - x2-1 is concave up on interval (-1,1)^O (0,1) 0 (-1,0) U (1, 0 ).co (-∞, – 1)U…

A: Given, fx = xx2-1  We have to find the interval in which graph of  fx = xx2-1 is concave up.

Q: (a) Let f(x) = px² + 2qx +r with p > 0. By considering the minimum, prove that f(x) > 0 for all real…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 25. For the function f(x) = 45x3 - 3x5, determine the interval(s) for which f(x) decreases. O (3, 3)…

A: We will solve this question by  differentiating f(x) and then finding the intervals for which the…

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

A:

Q: 16. Suppose that f is differentiable at c and that f'(c) + 0. Show that there exists a ð > 0 such…

A:

Q: 3. Let f(x) = x, given the interval [0,1]

A: fx=x, x∈0,1 f'x=1&gt;0 for all x∈0,1 So, fx is strictly increasing on the interval 0,1.

Q: of and ду of For the function f(x,y) = In (x+ 3y), find

A:

Q: Determine the types of singularities of the function f(z)=1-e^2z/z^4

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Q: • Use the IVP to prove that r3 – 4z+2 has a zero in the interval [0, 1] • Use the IVP (and a similar…

A:

Q: 2. Let f(x) = S dt for x 2 2 In a) Find F'(x). b) Is F increasing or decreasing? What can you say…

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Q: 0 if x V2. Prove or disprove that f is continuous.

A:

Q: (a) Let f: R" → R be a function given by f(x₁, 2,...,xn) = x²₁₁x²2x², where n = 1. Show that the…

A:

Q: {(u)= (u² -3)*

A: Given the function is  f(u) = 12u2-32. We have to find f'(u).

Q: (a) Let f: R→ R be a function given by f(x1,x2,...,xn) = x².x²...x², where n = 1. Show that the…

A: Note: since you have posted multiple questions. As per our guidelines we are supposed to solve only…

Q: (a) Prove that, for every c E [0, 0), the equation xe" (b) Suppose f :R → R is a continuous function…

A: This is problem of Real Analysis, topology.

Q: a. Determine if the function is concave, convex or neither. f (x1, x2) = (x1 – x2)². (25 – 20x1 –…

A: Part(a): Given, fx1,x2=x1-x2225-20x1-16x1x2+12x22 Now, solving the given equation,…

Q: (b). Show that iff= u+iv is analytic in a region S and u is a constant function (i.e., independent…

A:

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

A: Solution

Q: The graph of f(x)= x2 - 1 is concave down on interval | (-1,1) ^O (0,1) BO (-1,0) U (1, ∞ )co (- 00…

A: From the given problem:   fx=xx2-1   As we know that for concave downward:   f''x&lt;0   So,…

Q: let s(t)=3sin(2t)+5. find the absolute maximum and minimum of the function on the interval [0,2pi]

A: We have to find

Q: b. Test the continuity of the following function 1, x< 0 V1-x, 0sxs1 ,atx 0,1 x- 2, x21

A: We have to check the continuity of f(x) at x=0, 1

Q: 1. Employ the following methods to find the maximum of f(x) = 4x – 1.8x² + 1.2x – 0.3x* (a)…

A: Given f(x)=4x-1.8x2+1.2x3-0.3x4. To find: (a) find the maximum using golden search method.…

Q: (11) (C) For the function f(x) = x° – x, determine whether the hypothesis of Rolle's theorem hold on…

A:

Q: of of and ду For the function f(x,y) = In (7x + 9y), find

A: The given function,     f(x,y)=ln7x+9y

Q: The absolute maximum of f(x) =x² – 4x on [0,3] is y= OA. OB. 4- o 3- OC. OD. 0.

A:

Q: Q2. Show that F(x) = 3 – x², x € is contractive on its domain, but does not have any fixed points.…

A: To show - Show that Fx = 3 - x2, x ∈ -14, 14 is contractive on its domain, but does not have any…

Q: A natural cubic spline S for a function f i defined by: x3 x2 - 12 4 3. S(x) = x3 3x2 + ах 4 17 + ax…

A:

Q: 5. Verify first that the Intermediate Value Theorem applies to the indicated interval and find the…

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Q: 5. Show that the function h(x, y) defined by 1 if a? + y? 1 is discontinuous.

A: We can solve this using R.H.L ≠ R.H.L

Q: Find the absolute maximum and absolute minimum of f(z) = +z - 48z over the interval (4, 8).

A: We have to find the absolute maximum and absolute minimum for the function f(x)=x33+x2-48x over the…

Q: Determine the maximum value of f (x) = 5x – e5x [T:3] on the interval [-1,1] %3D

A:

Q: b

A:

Q: Find aland U so that the function S 7z³ – 3x² + 7, z -2 is both continuous and differentiable. al =

A: To Determine: fins a and b so that the function is continuous and differentiable given: we have a…

Q: If Tn,0(x) = ao +a¡x+ a2x² +.. he function f(x) centered at x = %3D -) True p) False

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: 3. (10 points) Determine the value of C such that if r +0 f(r) := V16 + 3x – 4 if r = 0 will be a…

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Q: A function ƒ is continuous for all x and has a local minimum at (2, –5). W statement below must be…

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Q: Q-2-for what valne of b is x+2b gex)=- 2 x²_b b-3 2. Continuous at every x ?

A:

Q: 1. Show (in terms of -5) that a function f: [2, 7] R be defined by f(r) V+1 is uniformly continuous.

A:

Q: 4. Are the following functions cubic splines? a. f(x) - x- 2x + 3, 0 sxs 1, - 2x - 3x2 + x + 2, 1 s…

A: Given :(a) f(x)=x3-2x+3, 0≤x≤1             =2x3-3x2+x+2, 1≤x≤2(b) f(x)=5x3-3x2+1 0≤x≤1…

Q: 2.23 Let 1 - x2 f(x): if x € Q, if r ¢ Q. Find all points p at which f is continuous. Prove your…

A:

Q: 1. Consider the function z = f(x, y). If fa(a, b) and fy(a, b) both exist, and they are equal, then…

A: 1. Given: z=fx,y and suppose that fxa,b and fya,b both exists and they are equal and it is…

Q: Suppose f is a differentiable function on an interval II and f(x) 6= 0 for every x in the interval.…

A:

Q: 3. Show that there does not exist a non-constant continuous function f : R2 → R such that f(x, y) =…

A: Given:- f: R2→R

Q: of of and Find dy for the following function. f(x,y) 3 е 4xу In (6у) of of II

A: If the function is a multi-variable function then to find the derivative with respect to one…

Q: 1-x², x 2 at x = 2.

A: Given, fx=1-12x2, x&lt;23,    x=2x-2-1,   x&gt;2

Q: 3. Let f)=x+x+2x-1E2,lx). Then x= 1 is a root for r() of mmltiplicity 3D1 None 4 2

A:

Q: 16. Consider the function f:(-2, 0) → [0, 0) defined by f (x) = vx +2. Prove that f is injective.

A: f(x) here is injective if and only if for all a,b∈(-2, ∞) we have a=b⇔f(a)=f(b)