1 Find Maclaurin polynomial P, to ƒ (x )= 1 1 sin Ax cosx 1-x 1+x

Q: 2. Without specifically finding its roots, show that f(x) = 0 for some x E [1, 2] where x2 4 f(x) =…

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Q: Find all values of x in the interval [0, 2π] that satisfy (cos x)2 − 3 sin x − 3 = 0

A: x=3π2 is the only values that satisfy the given condition see the calculation below

Q: 4 35₂ In evaluating 2 dx X√√x²-4 is same as evaluating lim cos-¹(f(x)). Determine the value of f(x)…

A: We have to find the value of f(x) at x= 2.9.

Q: Prove that J5/2(x) = 2 TCX CScanned with CamScanner 3-x² 2 sin x - 3 COS X

A: Use the given information.

Q: 5. Show that cos x = x has a solution in the interval [0, 1]. Hint: Show that f(x): = X cos x has a…

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Q: Find the critical numbers of the function. g(x)%3D8X+sin 8x

A: Given query is to find the critical numbers for the function.

Q: a. Let ƒ(x) be a function satisfying 0 ƒ(x) 0 … x2 for -1 … x … 1.Show that ƒ is differentiable at x…

A: The differentiability of the function can be determined with the help of the left-hand derivative…

Q: 1. Find the critical numbers of f(x) = 2 cos(r) + sin (x) %3D

A: Given: f(x)=2cosx+sin2x  A number is critical if it makes the derivative of the expression equal 0,…

Q: Determine whether f '(0) exists. {: x2 sin 4 if x + 0 f(x) = if x = 0 f '(0) does exist. O f '(0)…

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Q: 1 Find Maclaurin polynomial P, to f (x )= : 1 1 cosx sin Ax 1-x 1+x

A: According to bartleby guideliness we can answer only the first three subparts of a question. kindly…

Q: 1. Find the fourth Maclaurin polynomial for f (x)= sin 2x.

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Q: 4. Show that f(x) = sin(x² + 3x) is equal to g(x) = -x cos(x) at least once on %3D Hint: Think about…

A: Given that, f(x) =sin(x3+3x),  g(x) =-xcos(x) Given an interval as -π,-π6 To show that f(x) and g(x)…

Q: x2 – 1 - if x <1 x – 1 - f(x) = T In x a cos 2rx + b sin(- 4 In 2 if 1<x < 4 if 4 < x where a and b…

A: Explanation of the answer is as follows

Q: Prove that for all x € [1, 00), – sinh (- |cosh¯'(x)|) = Vx² – 1.

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Q: #2. Verify Clairaut's Theorem for the given function f (s, t)= In (st)-s* sin (6t) +st.

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Q: 1. Sketch the graph of f(x) = cosx on 0x< and use your sketch to find the absolute and local minimum…

A: Lets make a table for y=cos xWe pick known values of x and find y for them. Then convert them into…

Q: 3.4 Find the residue of f(z) = (1 – 2®) sin(1/z). %3D

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Q: 22. Determine f(x) so that cos(In²x) f(x) dx = sin(In²x) + C (a) 2 In x 2 In x (b) Inx (e) NIK

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Q: The German mathematician Karl Weierstrass (1815-1897) noticed that the substitution t = tan(x/2)…

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Q: We have f(x): f(x) = {sin2x 0 >ܝ TT 2 <x< O. W. a)find the coefficients and show that Vx € [-^,^]:…

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Q: 1+ In x Find f(x) so that when u f(x) the integral tan( fx) dx can be rewritten as cot u du. A) x-…

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Q: 4 35₂² In evaluating 2 dx x√√x²-4 is same as evaluating lim cos-¹(f(x)). Determine the value of f(x)…

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Q: Show that cos x = x has a solution in the interval [0, 1]. Hint: Show that          f(x) = x - cosx…

A: As the intermediate value theorem states that if a function is continuous on a closed interval [a,b]…

Q: - Find the extreme value/s of f(x) = 4 sin² x cos 2x on (37 3π 5π 22

A: This is a problem related to maxima and minima of the function. Based on the general formula and…

Q: 4.4. Show that the function f(x) = Sx² cos 1, if x = 0, ૨૦. if x = 0 is a BV-function over the…

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Q: Define h(x) = x³ sin(1/x) for x + 0 and h(0) = 0. By using the product and chain rule we know that…

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Q: 7 Use the Intermediate Value Theorem and Rolle's Theorem to show that the equation 2 = sin z+1 has a…

A: use the intermediate value theorem and Roll's theorem to show that the eqautionx2=sinx+1has a…

Q: 15. Suppose that F'(x) = 3x + cos(r - 1) and F(1) = 5. Then find what F(x) is precisely.

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Q: 9. The value of f 1-x 1+x A. sin ¹¹x + √1 + B. sin¹x - √1 + dx x² + C x² + C C. sin ¹¹x + √1- x² + C…

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Q: 1. Show that f(x)= 4 sin(44)+2-x has at least one zero on (-1,0J. %3D

A: we have to show that there exists at least one zero of a function f(x)=4sin(πx2)+2-x on an interval…

Q: 1-cos 2kx 3. Find k such that f (x) = x2 is continuous everywhere. 4 - 7k X = 0

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Q: Find the root of f(n) = 3x - cos(x) -1 = 0

A: Please rate and feel free to ask any query about any part.

Q: sin 7Z „Find the residue of f (z)at z = 4 (z – 4)? Let f (z) =

A: Note:

Q: The limit lim (18 x; - 28 sin (x;)) Ax i=1 on the interval 0, is equal Tt/4 | (9 x² + 28 cos (x)) dx…

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Q: Locate a root of: f(x) = sin x + cos(1+x²) – 1 Using secant method with initial guesses xo = 1.5 and…

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Q: 7. Determine f (x) so that | cos(In°x) f (x) dx = sin(In²x) + C 2 In x In x (а) 2 In x (c) - (d)?

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Q: 9. The German mathematician Karl Weierstrass (1815-1897) noticed that the substitution t tan(x/2)…

A: Solve the problem

Q: Consider the function given by V2 + x x² – 4 x<-2 g(x) = -2 <x<0. x + 2 2 sin(7x) 0<x Determine if…

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Q: A. Ifw=sin(x+bt)+cos(2x+ 2bt). Prove that =6? B. If f = x*y* + 2y sinx + x²lny then show that fxy =…

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Q: 7 a Show that for all positive integers n: 27 2n sin nx dx = 0 ii cos nx dx = 0

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Q: Consider the following equation. cos x= x (a) Prove that the equation has at least one real root.…

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Q: (b) Prove that 2 -3/2 Js12 (x)dx = sin xy + C. 'COS X x2 x3

A: We have to prove ∫x-32J52(x)dx=2πcosxx2-sinxx3+C

Q: Express the limit lim (3 cos (2ra* ) + 4)A¤¡ over [6, 8] as an integral. 2 CoS n- 00 i=1 9. Provide…

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Q: The f sin x cos²xdx is x sin 4x {A} 16 64 sin 4x x {B} 16 16 O A B O - sin³2x 48 sin³2x 48 +C + C…

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Q: sin TZ Let f (z) = Find the (z – 10)² residue of f (2)at z = 10. -

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Q: 1. Determine the smallest positive root of f(x) = Sin x + Cos ( 1+ x ) - 1. Use 5 %3D iterations of…

A: Given function is f(x)=sinx+cos(1+x2)-1 the graph of the function is From the graph we can see that…

Q: 4. Verify Rolle's theorem in the following cases (a) f(x) = (x – a)m (x – b)", where m and n are…

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Q: Find any critical numbers of the given functions 1. f(x) = x* - 4x² 2. g(x) = 4x x2+1 3. h(x) =…

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Q: 5 find aroot of the eqution f(x)=x²-4 Sinx = 0 using the 2 Newton-Raphson, Xo = 3,6=0.0005

A: Given equation is f(x)=x2-4sin(x) Initial approximation is x0=3 Now f'(x)=2x-4cos(x) formula for…

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…