• Example Evaluate fx) dx if x < 2 | 3x – 2. *22 f(x) = Solution See Fieure 565. From Theorem 555 we can inteerate from 0 to 2 and from

Q: = - 1) ex²-x dx x. Use the substitution method to rewrite the function in the integrand, (18x – 1)…

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Q: 1. Find f' (0) given that f(x) = sinh-1 e*.

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Q: | sinh$4x cosh 4x dx can best be evaluated by General Power Formula. A True B False

A: Explanation of the answer is as follows

Q: 28+1 b:If y =-1 prove that. 1- 2y dx

A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: b) [F(x) then find f(x). If 3 In(x)/ sin(3x) − 3e³ + x² + 3. - f(x)dx= 3 ln([x]) + 3x + C

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Q: If e/2i =sin2 then z = - 2 In(sin2) + 4k t – 2i In(sin2) + 4k T

A: Equation can be solved by taking natural log both sides

Q: If f(x) = sinh³ x %3D the en f'(x) = ||

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Q: To evaluate 3cos x=1 dr. the integrand can be transformed to 1-sin2x A.) S(3cos³x + csc?x)dx B.) 3…

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Q: i need the answer quickly

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Q: Determine whether it converges or diverges. You must provide justification for your answer. |…

A: Answer is yes its convergent .

Q: A ( sinh x- coshx tanh e 6)

A: You all need to have the idea of hyperbolic and their basic calculus.

Q: dx Evaluate x²/4 x²

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Q: Ax) = Ln=0 n! e Show that: GAx)dx = En=1 n(n+1) (–2)"-1 (n +2)! ||

A: Here we use integration and series theorems to find the solution.

Q: a) sin2021 (2mr)dr re gln z b) Ip- c) | In(csc r) cot rdr 1 d) 2r – a2 et - e- dr ez +e- e) 을 In 3…

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Q: 1. S Vcos 20 sin 20 d0 x²-x 2. S- dp- (x+1)

A: To  evaluate the integral.

Q: 3cos3x - 1 To evaluate dx, the integrand can be transformed to 1- sin?x

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Q: Find the linear approximation of f(x)=cos(x) at x=3π/4 and use it to approximate cos(137∘). Give…

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Q: 2*csch( 2*) d x cosh(2*)-sinh(2*)

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Q: (5tan28 etan 28 sec² 2 Bd B

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Q: (/2 x cos" x dx, when n> 1, show that Jo If In п(п - 1)1,-2 — 1 In [Hint: cos" x= cos? x.cos"-2 x…

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Q: :S- iven : alue of AB 3 8x+1 4x- dx. If we let the substitution" = 4x-5, the final answer takes the…

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Q: 1 Proof (I): (sinhx)' = Vx? +1

A: Given: The equation is sinh-1x'=1x2+1. To prove: The main aim is to prove the equation. Concept: The…

Q: se the bisection method to solve the equation x + cos x = 0. Show an appropriate graph. a. b.…

A: The bisection method uses the midpoint of an interval to perform the iterations to approximate the…

Q: sin 2t sin 5t 10 58s2+ 441 20 s4+58s2 +441 84 O Option 3 Optlon 4 O Option 2 O Nons of the cholcss…

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

A: Consider  Where x belongs to the interval [0, 1] Since x and cos x both are continuous on [0, 1].…

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: Evaluate. d farctan a – In a] dæ 1+x² 1 sec2 x 1 :- e" sec² ¤ 1 + 1-x²

A: The rule of derivatives states that ddx(f(x)±g(x))=ddx(f(x))±ddx(g(x))

Q: Q-6: Evaluate the integral 1). dx So Jie-1

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Q: The fixed point iteration rn+1 = xn + sin(xn) has roots at r = nn %3D

A: In this question, the iterative scheme is given as xn+1=xn+sin(xn) The root of this equation r=nπ…

Q: Test the ff ODE for exactness and find the general solution of the DE. (2x + 3y) dx + (3x + 4y) dy –…

A: Let's find.

Q: (22 – 2) | Evaluate dx 2+2 (x4+5x2 +4) tan1 2 A - BI E E E E X O Type here to search 马

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Q: (A very cute proof ) I want you to show using integration by parts that sin(mx) sin(nx) dx = 0 if m…

A: To show: ∫0πsin(mx) sin(nx) dx = 0 We know that, Integration by parts ∫u dv = uv - ∫v du Suppose, u…

Q: 2 +3 Evaluate S4) (-2) (22+4)(- dx. Enter In(x) for In(x), abs(x) for |x|, and arctan(x) for…

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Q: 3. Prove that -2/3 dx diverges by showing that х lim -2/3 dx = 00 х

A: Given limit is Since one of the limit of integration is infinite , so we evaluate the limit as…

Q: Solve fllowing D E the y+4y= Cos x- sin X

A: Recall the trigonometric identity: cos2x - sin2x = cos2x Hence, we are necessarily trying to solve:…

Q: .2 1 2x -1 Prove that : sin .2 dx = 72 1+x 1+x?

A: Solution of given question is given step by step

Q: GUESTION 3 dy Fmid Tx 2. 3.1 sinh e 3.2 %3D (Simiplify = Sech Cuox) answer fully your

A: Given

Q: 6. S(x)= In(tanh 5"

A: As per bartleby guidelines we only give first question answers.

Q: 4. The given equation sinh(xyz) = x + y + 3z implicitly defines a differen- az tiable z as a…

A: Differentiate with respect to x keeping y as a constant.

Q: 3. Determine the values of 0 if 0 < 0 < 2n given that cosx process. - 0.3178. Explain your

A: When considering the circle our degree values changes from 0 to 360. So we know in which quadrant…

Q: QUESTION 5 10 If continuous and Jx)dx = 54, then which one of the following numbers can take at…

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Q: /4 1. evaluate [sec(x) dx . Give 3 decimal places for your answer. If your answer is below 1, use a…

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Q: 47. Let y = sec-x. Show that tan y = vx? – 1 if x > 1 and that tan y = -Vx? – 1 if x 0 on (0, 3)…

A: Consider the function of x and solve further-

Q: B ) if y= sinh¬1x then prove that =

A: Given y = sinh-1(x)sinh(y) = x On differentiating both sides , we get sinh(y)' = (x)'(cosh(y))dydx…

Q: 1 In order to evaluate dx, the correct substitution is V-x²–4x+21 None of these -2 + 5 sin(t) x = -2…

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Q: 2x csch (2*) cosh(2*)-sinh(2*)

A: Note: since you have posted multiple questions. As per our guidelines we are supposed to solve only…

Q: Evaluate *(x-2) dx (x-1)3

A: We can find the required answer in the following steps

Q: 6. Using a suitable substitution in each case, integrate the following w 1 (a) x2 + 10x + 29 sec?,…

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Q: e Lim 2. 5+s2 y4 3 Lim (4) Lipn J+ Cos늦

A: 1. lims→∞(ss+1)(s25+s2)lims→∞s×s2s×s211+1s11+5s2= 12×2=14

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.