1 1 [X1 X2 Ex + 'x] and B = X2 - X3 [2x1-x21 7. Determine [T]B_ if T

Q: how can i show that  t/(1+t2 )-tan-10  algebraically?

A: Let gt=t1+t2-tan-1t

Q: 16. f(x) = x' + x + 4 on (-1,2). 17. f(x) = x -x² – 30x + 3 on (0, 6). 18. f(x) = 3 sinx on [T/4,…

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Q: 3) Prove that c) cosh2x = 1 + 2 sinh? x

A: In the question we have to prove the given function.

Q: 2. Find an interval where f,(x) = sin2 x and f2(x) = cos² x are linearly independent. %3D

A: W(π/4) = -sin(π/2) = -1 W(π/6) = -sin(π/3) = - √3/2 Since, Wronskian is not zero for a single value…

Q: 4. Find az/ax if z is a two variables function in x and y is defined implicitly by x5 + y² cos(x²₂³)…

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Q: Find f'(x). f(x) = O O O 6x - sin² (5x) f'(x) = O f'(x) = f'(x) = f'(x) = = 6-10sin(5x)cos(5x) 2√6x…

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Q: 1 If f(x,y,z)= of then x-y-3-

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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: iii) E(-1)"+1 cos²(÷) COS n=1

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Q: Suppose that 2x² - y² = t² and x = t cos 0. Find (a). ¹(2), X and 0

A: answer is in next step

Q: 0.2 Differentiate In x+1, with respect to x. x²-x+1

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Q: 1. If f(x, y)=3x' sin y- y² cos x- 2yln x– xh y- 4xy , find- of ôf ô²ƒ ô²ƒ

A: Given: fx,y=3x3siny-y2cosx-2ylnx-xlny-4xy2

Q: 5. If y= tan x, prove that y``=2(1+ y² )(3+ y²).

A: Prove the given equation

Q: In(x²) + 6 Consider the continuous function h with h'(x) = 3 3.1 Find and represent the domain of…

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Q: -1-3x+ e3X ) im x>0 hint: L'Hopitals Rule - cos(x)

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Q: Compute[x² sin(2x)dx. A.- x² cos(2x)+ xsin(2x)+ cos(2x)+C 1 1 B. — — x² cos(2x)+ —…

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Q: Differentiate y=excos(x2): y'= A. excos(x2)-2xsin(x2) B. -2xexsin(x2) C. ex(cos(x2)-2xsin(x2))…

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Q: 5. Show that the function f (x) has roots between (0,2) x² + 2x – 3 f(x) x - 1

A: To show the f(x) has roots between a and b we have to show that

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: 7). Suppose a is a positive constant less than T. Prove that the equation 2x+cos x = a has a real…

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Q: 4. A force of F(x) = x - cos(3x) + 2,x is in meters, acts on an object. Identify the work required…

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Q: (§5.4, Q42) Calculate So™ f(x) dx, where sin x, x T

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Q: 3. Find the critical numbers of the function f(x) = sin2 3x + cos 3x , 0 <x < 2/3:

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Q: We have determined that g'(x) = 2 and h'(x) = cos(x), where g(x) = 2 In(x) and h(x) = sin(x).…

A: Our Objective is to find the derivative.

Q: If f(x) = sin(x)e2x, then f"(x) = A) 3sin(x) e2x + 4cos(x) e²*. B) 3sin(x) e2x + 2cos(x) e²x. C)…

A: The given function is: f(x)=sin(x)e2x to find the second derivative f''(x). For that one has to find…

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

A: Given, Cosx =x

Q: 1-2x²=1+x+x²³ 2²-2²-1+2+ -2(-1) (2n + 1)! x²+1 sin x- ---- cos x=(-1). - (2n)! −2+4- 6! tan 'x-…

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Q: (2) If y = (sin-1(x))², prove that (1- x2)y" – xy' - 2 = 0.

A: here first we will derivative with respect to x then squaring both side and put value of the y then…

Q: find | cos*x dx 1 1 1 А) — — х —- sin2x + —x + — sin4x + c 4 1 B) =-x +- sin2x + X 4 1 8 1 x + sin4x…

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Q: If  f(x,y,z)=ln(x2y+sin2(x+y))+227x228y2z229,  then    ∂4f ∂x2∂y∂z at (1,1,1)  is equal to

A: See the attachment.

Q: (e²)(sin²2x) Compute In y and In 5z

A: Basic log formula are applied to solve the question.

Q: 1. Evaluate f sin*(2x + 3)cos (2x + 3) dx sin(2x + 3) put = t 2. Evaluate f dx Put x2 + 5 = t x2+5…

A: Explanation of the solution is given below.....

Q: 6xsec 3x 2-If y = (tan3x)²² prove that = (tan3x)²= + 2ln(tan3x) %3D dx tan3x

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Q: Show that y1(t) = cos(3t) and y2(t) = sin(3t) are linearly independent for all t

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Q: 1. Find the critical points forf (x) = x + %3D

A: Dear student as per our rule in one session we can only solve one question. Please post the other…

Q: 12. Let f (x) = x + find all the critical %3D points and use the second derivative test to prove if…

A: We have to find critical points and state whether they are maximum or minimum using second…

Q: Find 2 if x? cos4 cos* T. 1) 2xcos x+4x2cos3xsinx 2) 2xcos x- 4x²cos³xsinx O3) 2xsinx sin xcosx 4)…

A: Hence option (2) is correct.

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: 5. Show that the function f (x) has roots between (0,2) x² + 2x – 3 f (x) = X - 1

A: Given that

Q: Find f'(x): f(x) = sin(2x) O 4sin (2a) (2 ln 4) cos(2x) O 4sin (2x) (2 cos(2x)) O 4sin (2x) (In 2)…

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Q: 2. For the continuous time periodic signal x (t) = 2 + cos(# t) + sin( t) determine the fundamental…

A: Given continuous time periodic signal is x(t)=2+cos2π3t+sin5π4t                            (1) The…

Q: .2 Suppose that w = x² + y² – z2 And x = psin(4)cos(0), y = psin(4)sin(0), z = pcos(4) Use…

A: The Solution is given in next steps

Q: 5.f(x) = x (x - 1)(*- 2)(* + 1) As x + +o, f(x) = As x - -n, /(x) As x > I co, f(x) – As x > w./(x)…

A: Solution is given below:

Q: Apply Definition 1.4 of Chapter IV to show that the function f(x) = 3x + 2 is integrable on the…

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Q: Find domain and range of the funetion f(x, y) In[e-x' -y'1

A: The ln function is undefined for negative arguments. This will ensure that argument is positive. So…

Q: If f(x)=sin-'x. Show that (1-x2) fx(x)-xf (x)=0. HENCE ,prove that f^(n+2)(0)=n²f^n(0)

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Q: 3 – 2ry' + 2y = x° sin x

A: The general solution will be the sum of the complementary solution and particular solution.   The…

Q: H.co/ prove That;. dz 1-2 Cosh2=

A: