2. Let f be continuous and differentiable everywhere. Suppose that f has zeros at 1 and 3. Show that there are two distinct real numbers r1 and r2 such that f'(r1) =-f'(x2).

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Q: 9. f(x) = cOs x, a =

A: Follow the procedure given below.

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A: We have to find radius and interval of convergence.

Q: Find the area of the following triangle, OA= 40 OA=80/3 O A= 80 O A= 40/3 RI TH

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Q: 8. Differentiate each function. Express your answer in a simplified factored form a. f(x) = (x +…

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A: Given:      x225+y216=1

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Q: (d) All identity matrices are diagonal matrices and vice versa. (e) All reduced row echelon matrices…

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A: Double integral

Q: Find the remaining trigonometric ratios. Зл T < x < 2 1 cos(x) %3D sin(x) tan(x) %3D %3D cot(x)…

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Q: Consider the following lines 4:z=1,y-1=-4,2=1-3t :z=28+1,y=1-3s,2=1 -y+1 %3D z-1 3a 2a 3 Find the…

A: Explanation of the answer is as follows

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A: Given query is to find series converges or diverges.

Q: > (-1)" x3n+2 find the exact value of 5-1)"(3n + 2) By differentiating the power series 8n n=0 n=0

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A: It is given that Acme Widget Company has found that if widgets are priced at $125, then 2700 will be…

Q: x³ + x2 – 4 1. Consider the function f(x) 4.x = x +1+ Note that x² – 4 x² – 4 - x²(x² – 12) (x² –…

A: Solution is given below:

Q: 3. -2 -5 Find the va lue of Hif Xi+xdx 3.

A: 3-2-518H-134=∫03x1+x2dxPut 1+x2=yas x →0 ,y→1as x →3 ,y→2differentiate on both…

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Q: 2. Use the Mean Value Theorem to show that f(r) = 2x sinh(x – 1) + 2" – x has a critical number…

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Q: Given the function f(x) = () a) Find a power series representation for f(z). п(п + 1) (n + 2):…

A: Let's find.

Q: (a – x)°dx S(4x + 1)°dx

A: use the substitution method for solving the integral.

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A: Given system of equation…

Q: Find the coordinates (x,y) of the given angles. 1. 10n 4. 45* 5. 270 3. - Sm 6. 330°

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Q: CURRENT OBJECTIVE Apply L'Hospital's rule to find the limit of an indeterminate form produced by a…

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Q: Problem 2. Which gives the inverse transforms of the given s-domain function? s2-s3+3/s3(s+5)(s-2)

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Q: 1. Which of the following is a convergent p-series? (A) n³ n=1 n (B) 3 n=1 1 (C) n=1 3 1 (D) n n=1

A: A) ∑n=1∞ n3     Since n is positive integer⇒  The above series diverges B) ∑n=1∞13n   It is not p…

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Q: Given functions f and g are periodic. Identify whether the following functions are periodic. i. ii.…

A: Take the two examples of periodic functions and then solve.

Q: 4 3 1 10 15 20 25 30 35 time (sec) feet velocity (ft/sec)

A: At t=0, velocity is 1 ft/sec. At t=25, velocity is 3 ft/sec. Required distance =Final velocity -…

Q: Test the series for convergence or divergence. n=1 n35n (n+ 2)!

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Q: A follasng vector fiebdo are conserva hal function. c)

A: We have to find the potential function if the given vectors are conservative vector field

Q: Use Part I of the Fundamental Theorem of Calculus to find each of the following when f(x) = | t*dt…

A: By using Part I of the Fundamental Theorem of Calculus:f'(x)=x4

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A: Given that the ice-cream factory makes two flavors creamy vanilla and Continental mocha. It is given…

Q: find the total derivative of z = f(x,y) = 2x+xy-y2 where x=g(y)=3y2

A: Given function: z=2x+xy-y2 where x=3y2 Putting the value of x in z , we get…

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Maximize…

A: To use Lagrange multipliers to find the indicated exrema, assuming that x and y are…

Q: Under a change of variables æ = u², y= v³ , the infinitesimal element of area dædy becomes 3u?u°dudv…

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