x, (a) x= 19. f(x) = 1, 1>2 sided 2 3-x, x<2 20. f(x) =2, x/2, (a) x = X = 2 value 1 x> 2 21. f(x) ={x- 1' - 2x + 5, x 21 1-x, x* -1 (a) x 12, 22. f(x) = X= -1 value

Q: 2 A manufacturer makes a product, of which the principal ingredient is a chemical, X. moment, the…

A: From the given data, State of nature Course of action    S1 (Use Y and Z) S2 (Use X)…

Q: Suppose (1,1) is a critical point of a function f with continuous second derivatives and fz = 44,…

A:

Q: 2/3 Q31 3x-2x, [-1,1] =3(x)-2 2- -1/3 -1/3 2x 2(x"?-1)=0 -1/3

A:

Q: What is the critical point of the function f (x) = cos x? 2. What is the maximum point of the…

A:

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

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Q: Give an example showing that, even if f 0 (c) = 0, it could happen that f(x) does not have a local…

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Q: 4) Find the critical points of the function f(x) = x²- 9 x* + 15x +3 and identify their nature. Draw…

A: Given that: f(x)=x3-9x2+15x+3 The graph is shown below

Q: .3 X ナメ-2 find x using fixed point method where X= 015 (initial Value)

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A:

Q: A basketball player makes a successful shot from the free throw line. Suppose that the path of the…

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Q: x* + 2x – 4 3 x' + 3 x²

A: The solution are next step

Q: The critical numbers z = 1 and x = -2 are found from a continuous function f' (z). Given that the…

A: The Solution is given below

Q: In Problems 23–38, for the given functions f and g, find:(a) f ∘ g (b) g ∘ f (c) f ∘ f (d) g ∘…

A: In Problems 23–38, for the given functions f and g, find: (a) f ∘ g (b) g ∘ f (c) f ∘ f (d) g ∘ g…

Q: dN₁ dt dN₂ dt 5N₁ 1 N₁ 20 N₂ 17 9N₂ 1-- N₂ 20 N₁ 17 1.6- 0.6-

A: This is a question of the equlibrium of the system.

Q: Use algebraic methods to determine the critical value(s) of f(x)= x/(x^2-x-2). Give your answers in…

A:

Q: find all critical points of the function f (x) = x ln x

A: Given: First, take the derivative equals to zero. Therefore,

Q: 1. Find the maximum and the minimum values of the function f(x)= 2x – tanx %3D in the interval 3' 3

A: Given: f(x)=2x-tanx Differentiate the function with respect to x. f'(x)=ddx(2x-tanx)=2-sec2x…

Q: If Newton's method is used to find the critical number of f(x) = x® – x³ +x² – 2x with initial…

A:

Q: 5. [ 4 ifx2 Show that f(x) = is not differentiable at x = 2.

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

Q: If the function f(x,y) is continuous near the point (a,b), then at least one solution of the…

A: Solution:-

Q: 3. Use Rolle's Theorem to show that the function f (x) = x² sin(x) – x sin(x) has a critical point…

A: For y = f(x). Let f(x) is continuous at every point of the closed interval [a, b] and differentiable…

Q: f(x)=(-0.7x2+6.8x+4.2)e-x^2 Find the critical points, inflection points and intercepts (if any)…

A: Critical points of a function are those points where the derivative is zero and the point should lie…

Q: What are the critical points of sin(x2-1), at the closed interval [-1,1]?

A: Given: The critical point is a funtion is the point where the derivative of the funtion is zero.…

Q: 19-While calculating the approximate solutions of the equation f (x) = 0 using the initial value of…

A:

Q: The stock price for a certain corporation can be approximated for the years 2007 through 2015 by…

A: At the point of local minima or Maxima the derivative vanishes.

Q: Prove: cosh 3x = 4 cosh° x x-3cosh.x

A: Prove that :- cosh 3x=4cosh3 x-3cosh x

Q: 1. Consider the function F(x) = x³(x – 2)². a) Find all x values where F'(x) = 0 or F'(x) does not…

A: Critical numbers.

Q: 3. The function f(x) = x^4 − 4x^3 + 8x has a critical point at x = 1.(a)  Find f"(x).   (b) Then use…

A:

Q: At time 0, M is deposited into Fund X, which accumulates at a force of interest δt = 0.006t2(0.006 t…

A: Given, δt=0.006t2 Now, we have, at=e∫0tδsds=e∫0t0.006s2ds=e0.003s30t=et3500

Q: The average rate of change of Ax) = x +x -x-1 over the interval o<xs1 is -2 1 O -1 2

A:

Q: 5. Find the critical numbers, and the intervals of increase/decrease for y=ln(4-x) %3D

A:

Q: Find the critical points of f(x)= (x 2-3)ex

A: Calculation: For critical points put first derivative of f equals to zero.

Q: 1-e2x 10. lim X0 1-ex x2-3x-28 4. lím エ→アーx-14x+49 11. lim In(x sin x) ズ→0 5. lim V2x + 1T ズ→4 12.…

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

Q: 1. f(x) = x² – 4x + 1 at point (0,1) 2. f(x) = x³ + 2 at point (1,3) 3. f(x) = 2x* + 3x³ – 2x + 7 at…

A: Given : The functions and the points.

Q: Q 3) Find the critical numbers of f(x) = x4(x - 1). Derivative Test' tell you about the behavior of…

A: given information function

Q: f(x) = lim (6x + 2 4x + 3) = 6x + 3 Ax-->0 f (x) = lim (6x + 2 4x + 2) = 6x + 2 %3D 4r-->0 f (x) =…

A:

Q: 1. Find all the critical numbers of the function (Justify Your Answer) (a) [5Vx – 2 f(x) = x > 2…

A:

Q: 6(2tanx - x^4 + 4lnx)^1/4(2sec^2x - 4x^3 +4/x)dx. Hint: let u = 2 tanx - x^4 + 4lnx

A:

Q: find the extreme values (absolute and local) of thefunction over its natural domain, and where they…

A: Given function:                         y=ex-e-x The domain of a function is the set of input values…

Q: (y-x)=y-x+ 2; y=x+2√x+4 When y=x+2√x+4. Y' = Thus, in terms of x, (y-x)y' = y-x+2= Since the left…

A: If  y=x+2x+4 is a solution of (y-x)y'=y-x+2 then it must satisfy it.

Q: If the function f(x,y) is continuous near the point (a,b), then at least one solution of the…

A:

Q: 3/ Find the critical numbers of the function f(x)= x/5 (4-x)

A: The given function f(x)=x354-x

Q: x2-1 7) lím x--1 x+1 (x+4)ln(x+6) 8) lím x--4 9) lím x-0 Vx+5-V5 x2-16

A: Compute the limit as follows. limx→-1x2-1x+1=limx→-1x2-12x+1=limx→-1x+1x-1x+1…

Q: Hi, I need help with this step-by-step please.

A:

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

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Q: 2. Find all critical numbers for the function: g(x) = x/2x +1 B. 0. ÷.글 1 1 А. - - | 2 3 2 c. - D.…

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Q: Use algebraic methods to determine the critical value(s) of f(x) = x √4−x.  Give your answers in…

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Q: (2x - 2 x² - x f(x) = x² 4 graphing calcu x 2 x = 2

A:

Q: 8. x' + 10x² + 6x + 4 is concave down. 3 Determine the interval(s) at which f(x) = -- a) O(-1, 00)…

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Q: Suppose (-2,1) is a critical point of f(x, y) and that the Second Derivative Test applies to f(x,…

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.