Question 8 x² if x<2 Find the values of m differentiable everywhere. Let F(x) = { and that make f mx +b if x>2

Q: Question 20 How many antiderivatives does a function of the form f(x)=x" have when n*0₂ (A) 1 (B)…

A: Antiderivative means Integration

Q: Question 1: Show that u = f(x)g(y) where f(x) and g(y) are arbitrary twice differentiable function…

A: Method: partial derivative u with respect to x,y then substitute in the equation check weather…

Q: Question 12 10 If f is a continuous function and F'(x)= f(x) for all x E R, then x)dx=? 2[F(10) –…

A: We have to solve the problem

Q: Question#4: A box with an open top is to be constructed from a rectangular piece of cardboard with…

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Q: Question 18 Find the critical number(s) of the function. y- 3x +30x Select all that apply. 30 0. 3.…

A: We are authorized to solve only 1 question, please repost remaining questions Critical number

Q: QUESTION 6 f(x) 3D3 x*-4 x-12 x+1, has local maximum at x= 1 O8. 2- OC 2 D.

A: Find first and second derivative

Q: QUESTION 6 A critical point of the function occurs at an interior point c: when eitherf'(c) = 0 or f…

A: Critical Point:- A critical point is a point in the domain of the function where the function is…

Q: (x*, where f(x) ={ 2, x> a 1. lim my x = a. x, x < a (where 'a' is last two digits of your student…

A: (1) We rewrite the function with given information as, f(x)=x2    x&gt;252      x=25x      x&lt;25…

Q: QUESTION 1 Determine the symmetry of the function. f(x): to x² + 2 O Even О odd O Neither О Both

A: If f(-x)=f(x), even If f(-x)=-f(x), odd

Q: Question 35 ,x5 , find the value of k that will make f continuous on (-0,0) x-4 Given: f(x) = | kx²…

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Q: Question 5:Find the value of constant c, if f(x) is continuous at x = 2 |cx? + 2x if x 2 -

A: Given that: f(x)=cx2+2x    if x&lt;2x3-cx      if x≥2

Q: Question (1): Find the interval(s) for the function f(x) = x3 – 4x² + 5x where f is concave down,…

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Q: Question 1) Find the absolute maximum and minimum of the function f f (x, y) = yx² where - 2<x< 2 -…

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Q: QUESTION 3 Provide the slope of the line tangent to f-(x) at the point (-2,1) where f(x)= x5 +2x³ -…

A: slope of tangent line on  f-1 (x) is the derivative of f-1 (x) at the given point .

Q: Question 6 Sketch a continuous function with the following properties: The domain is [0, 4] Ax) > 0…

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Q: Question 9 Ay f (x) =< ; Estimate f (-2) %3D 8-6 4 O -1 -2 O None of these 2]

A: The graph of the function crosses the x-axis when x=-2. Then, the value of the function at x=-2 is…

Q: QUESTION 7 Consider a function f: R2 R, where f(xy) = x2 +y3. (a) Determine f(1,1) from definition.…

A: solve the following

Q: Question 1 Given f (x)=x-+2x-1 and bracket of 0, 1. Find the value of c that satisfies its…

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Q: Question 2 Given the function k with k'(x) - and b a real number such that b > 0. If the domain of…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Question: 4 Find the value of "k" such that the function f(x)=x² + kx-6 satisfies the hypothesis of…

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Q: 5 Question .4 Verify Mean Value Theorem for the function f(x) Vx in interval [0,9] Abc أدخل إجابتك

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Q: Question 4 Compute, step-by-step, the first and second derivatives and the maximum value of each…

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Q: Question 2. A function f(x) satisfies f(x+h)-f(x)=x+h+z² · h² + 4h³ for all z and h. Use Fermat's…

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

Q: Question 1 Let f(x) = 1 – xe(1-2). (a) Show that x = 1 is a root of f(x) with multiplicity 2.

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Q: Question 4: If you are given f(x) as follows: 1 if x -2 2 Show that f(x) is continuous at x = -2 ?

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Q: Question 11 a / f(x) dx: f(x) dx a True False Question 12 If f'(a) = 0, then the function f must…

A: Here we have to use the concept of integration and derivatives.

Q: Question 1 Let f (x) = Vr, a > 0. Prove using e - 8 methods that f is continuous at every point of…

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Q: Question 2 ( Consider 2x – a2; 0 4 2 - x; x - 4; %3D T; which statement below is correct regarding…

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Q: Question 1 • Let f(x) =1 – xe(1-z). (a) Show that x = 1 is a root of f (x) with multiplicity 2.

A: a. we have f(x) =1-xe1-xnow use the expansion of…

Q: Question 9 If f'(x) <0 for 1 <x < 6, then f is decreasing on the interval (1,6). True O False «…

A: We have to check

Q: Question 4: If you are given f(x) as follows: if x -2 2 Show that f(x) is continuous at x = -2 ?

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Q: Question 4. Continuity Exercise 2.5, Problem 26 a. Show that f has a removable discontinuity at x =…

A: We have to show f has removable discontinuity at x=3 and find the value of c

Q: Question 1 Consider the function y=x³ – 3x² + 2 (1) Find all the maximum and minimun points of the…

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Q: Problem 7. Suppose that the compler-differentiable function f: C has a primitive F on 2. Does it…

A: Suppose that the complex differentiable function f:R→ℂ has a primitive F on R then it may not follow…

Q: Question 38 The critical point of f (x) = (sin x) (cosa) on the interval (0, π/2) is at x = Ono…

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Q: Question 4 Consider :(-x, 2] → R, where f(x)=(x– 2)² +1. a. Define the function " x = 1,x = 5-V5 „*…

A: Since you have posted the different questions of parts. I am answering the first one. Please post…

Q: Question.2 Let f: [0,2] → R be a function f (x) = {x, ifx 1 Show that f is R – integrable. |

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Q: QUESTION 5 2 The absolute minimum of f(x)= 3 x3-2x 0n [-1,8] is y= OA OB5 OC OD.

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Q: QUESTION 6 Given the function f(x)=4x- 39x2+ 90x + 2. which of the following describes its absolute…

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Q: Question 32- of 33 Step 1 of 1 Given the following function, what is u' (x)? Treat F. Q, and W as…

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Q: a. Let f(x) = { 2 sin(2 – x) – 4, x 2. Is f differentiable at r = 2? b. Let (2h(x) + x)² f(x) = x +2…

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Q: QUESTION 4 Suppose f is differentiable at a; set d(x) = f(x) - f'(a)(x - a)-f(a). What is d' (a)? O…

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Q: Question 8 Suppose that H is a function of r satisfying H'(0) (1+-). N H" (r) – aH'(r) = 0, H'(0) =…

A: Given second order homogeneous differential equation : H''r-aH'r=0, where H is a function of r. To…

Q: Question 4. Given f(x) = x²/6 – x² on the interval [-V6, v6), find the intervals where f is…

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Q: Question 3. Find the absolute maximum and absolute minimum of the function f(x) = 3.x2/3 – x on the…

A: To find the absolute maxima and absolute minima of the following function  f(x) = 3x2/3 - x  in…

Q: Question 38. Suppose f : [0, 1] → R is a twice differentiable function that satisfies D² f (x)+…

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Q: QUESTION 11 Suppose f'(x) =x4+x3– 6x2. Determine the value of x where f has a relative maximum…

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Q: Question 3 Assume that g(r) be a function on (0, 100) and has a derivative g(z) and a primitive…

A: Fundamental  theorem of calculus part2   If f is a  real-valued function on a closed interval [a,b]…

Q: 8. Suppose you have a function f continuous on [0, 2] given by πχ f(x) = x + 2 sin(- 3 (a) Show that…

A: It is given that,  f is a continuous function on [0, 2]  defined as ; f(x) = x + 2sinπx3-1 + 1 a) We…