t0) = {Ax2 -1. [5x + 4, for x < 0, 4x2 - 1, for x20 10+

Q: 6. [T3] Prove the function f (x) = x³ – 5x² + 8x – 4 has an order two root at x=2, without using…

A:

Q: let f(x) = 2x^2+2x+3 and let q(h) = f(1+h) - f(1)/ h.    Then q(0.02) = ?

A:

Q: 1. Use the Intermediate Value Theorem to prove that the equation 3x - 4x² = 3 is solvable on the…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Determine the positive real numbers x and y such that • x + y = 4 and 2.n2 + y² is small as…

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Q: Show that x3 +x – 1 has a root in the interval [0,1]. (R

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Q: 1. and t= 1-X %3D 7. find at X= 2 10

A: Please refer the attached image for complete solution.

Q: Express f(z) = x-1-iy (x−1)² + y² in terms of z.

A:

Q: 15. With f(x) = 3x +1 and h(r) = 2x – 4, find (f oh)(5) - %3D

A: we know that  (fog)(x) = f (g(x))

Q: Which is equal to (x) given that g(x) = 1- 3x and h(x) = V?

A:

Q: Find the interval(s) where f(x) = 2x° – 15x? + 36x – 27 is increasing. -

A: The given function is fx=2x3-15x2+36x-27. The main objective is to find the intervals where the…

Q: If f(x, y) = 2x+6 (2a-6y) of then is given by:

A: In the above question we will take y as constant since we have to partially differentiate it with…

Q: Generate the approximation formula 1 f'(x) × - [4f(x+ h) – 3f(x) – f(x+2h)] 2h with the error term.

A: The objective is to generate the approximation formula,

Q: Find the value of c satisfying the conclusion of IVT (if it holds) given: f(x) = 4+2x- x² on the…

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Q: Find Valume x zO; Ekort the X3D2; 0 about the x- axis

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Q: Veridy that the approximate root of xa2 is: 1+Xn- Xn 2

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Q: Find f(x) iff, (p) Hence deduce F .

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Q: Use the intermediate value theorem to show that the equation x + 2x + 1 = 0 has a solution in the…

A:

Q: 4. Consider f(x) = 2x² + 3 on the closed interval I = [0, 4].

A: I have Provided this answer in step-2. i have given an only one answer because as per our policy.

Q: b) f(x) = x2-x %3D x²-1

A: To find out where the function is discontinous.

Q: Find all critical numbers of f (x) =8r³+39x²+ 18r– 4 (A -3, -

A: We have f(x) = 8x3+39x2+18x-4To identify the critical values, we differentiate and find values of x…

Q: 9. If f(x) = kx – 1 and f'(15) = 2, find k. %3D -

A: Given f(x)= kx3 - 1 and f-1(15)=2 then we have to find out the value of k

Q: Use the linear approximation (1 + x)k = 1 + kx to find anapproximation for the function ƒ(x) for…

A: Given: ƒ(x) = (4 + 3x)1/3

Q: -1, if -n <x<0 1, if 0sxSa h) f(x) = { %, -1<x<0 0<x<1 -x, if %3D if

A: We find Fourier coefficients then find required Fourier series.

Q: 4cos20 + 2/3 = 0 on the interval[0, 3t]

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Q: The function f(x) = x²e*- ex has a root in [0,2]

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Q: 1) Find the absolute extremum values of f(x)=x2-4x+20f(x)%3DX2-4x+20 over the interval [1,4][1,4].

A: The extrema value of  function is f(4)=20

Q: Q1) check the continuity of fX) at X- -1, 0,1.23 -1<x<1 2x-1, 3x-2 25x53 2, x=3

A:

Q: 3. Let f(x) = { ,x<2 ax + b, x22 Find a and b so that f (2) exists.

A: To find the value of a and b

Q: Find the particular solution determined by the initial condition. f'(x) = 3x273 - 6x; f(1) = - 7…

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Q: For all numbers x, x> 1/x counterexample

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Q: (b), f(x) = In (x² – 4)

A: Since you are asking only for b. Here is your answer.

Q: Discrete

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Q: Find the absolute extremum values of f(x) = x² – 3x + 8 over the interval [1, 3].

A: First we find critical value and then use first order derivative test.

Q: 6 4 Verify that for f(x, y) = 3x°y* - 4x°y°. дх ду ду дх of

A: Given problem:-

Q: If g (x) = 3x² + 12x – 96 on the interval [-8, 4]: What value of C satisfies Rolle's theorem?

A: here we have to use the result of the Rolle's theorem.

Q: 9x+5 Given that f (x) = find f-(x) AND prove by co 3

A:

Q: Given f(x)= x³ – 6x + 2 = 0 in the interval [-4,4]. By using Intermediate Value Theorem, determine…

A: Given  fx=x3-6x+2 And x fx -4 -38 -3 -7 -2 6 -1 7 0 2 1 -3 2 -2 3 11 4 42

Q: The Intermediate Value Theorem can be used to prove that the equation z² - 5x+6=0 has at least one…

A: Given :x2-5x+6=0

Q: -8x Since f'(x) then (x2 - 4)2' (x? – 4)>(D) - (-8x)[2cx? – 4)(Ox)] _ 8 x2 f"(x) (x2 (y2

A:

Q: Find a and b so that the function 2.3 – 5x² + 2, x -2 f(x) = ax + b, is both continuous and…

A:

Q: olve for t such that Tmix(t) = 100 degree F Tmix(t) = 72 + 65.8e^-0.125(t-tmilk) tmilk = 1.826

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

Q: V21. Show that there exist constants M and N such that M||x||| < ||||2< N ||x|| -

A: Given ||x||1=∑i=1n|xi|=|x1|+|x2|+...+|xn|       ||x||2=∑i=1n|xi|2=|x1|2+|x2|2+...+|xn|2 Now we have…

Q: 16. Let f(x) = x² + 10x + 28 m, find m if the function only has 1 (ONE) x-intercept. -

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Q: 5. Find the absolute maxima or minima for f(x) = x² + 8x + 3 over the open interval (-o, 0).

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Q: Find all values of x in the interval [0,2pi) 2sin^2x+5sinx-3=0

A: Given equation is, 2sin2x+5sin x -3=0

Q: Find the critical numbers of the function f(1) = 2x – 3x² = 36z. Answer (separate by commas).…

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Q: 3 By applying the Intermediate Value Theorem choose the interval over which x4 = 7x3 - 5 will have a…

A: The given problem is to find the interval for the given function that which the intermediate value…

Q: Find the value of c guaranteed by the Intermediate Value Theorem. x²+ 5x 9. 18 Ke) = 18 f(x) = f(c)…

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Q: Let h(x)=−2x^2+x+4/x^2+4x−1, what is h′(−5)?

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Q: Find the value of x if the matnx 1 5] 4 is Singular 2. A = -3 6. 2

A: