QI- Find the root of the functions within Ea < 4 % f(x) = e=*(3.2 sin(x) – 0.5 cos(x)) Given that x = 3, and xµ = 4.

Q: ELIMINATION OF ARBITRARY CONSTANTS

A: The given solution curve is y=C1excosx+C2exsinx=ex C1cosx+C2sinx. That means, the roots of auxiliary…

Q: bn= 는 Sin nT x dx ans=t- Excose LOS UTT sin

A: I have simplify and done step by step in detail...now hopefully you will get it.....go through the…

Q: Solving it with gamma and beta function 1 dx - Ln x

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Q: s Sinx Cosy 1-Sin" x elx

A: To evaluate the given integral.∫sin x cos x 1-sin4 x dx

Q: ropriate substitution, n³ (4x)cos*(4x)dx is equal to

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Q: f(x csc² 2x - x cos x cos 2x)dx

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Q: cos(x ) + æ5.1 dx. )ln(1+x² 3 cos(x Evaluate 1+ el.61x – 68 - 3. answer

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Q: sin 2n x Prove that: dx = 0 for all n e N. sin x

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Q: Prove the identity. sinh(x + y) = sinh(x) cosh(y) + cosh(x) sinh(y) sinh(x) cosh(y) + cosh(x)…

A: Given identity for proof is  Sinh(x+y) = Sinh(x)Cosh(y)+ Cosh(x)Sinh(y)

Q: cos x lim z-n/2 sin (2x)

A: If limx→afxgx is in 00 form or ∞∞ form; then applying L Hospitals' rule we get:…

Q: Evaluate the limit.

A: Given that, limh→0sin(2h)(1-cos h)h2 Because of the direct substitution of h = 0 into this, we get…

Q: II. Perform the integration. sinh (e-") dx e² cosh(e-¤) 4.

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Q: c Functions. Prove the identity cosh x – sinh x = e x-

A: We have to show the given condition

Q: tan ydy (1+ln(cosy))3/2

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Q: The value of i log (x -i) + i? n + i³ log (x + i) + i* (2 tan-'x) where x > 0 and i = Fis

A: Introduction :

Q: ph of y = cos x from x = 0 to x = 27 by making a table using multiples of #/2 for x. y= cos x 2 EIN

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Q: sin x Check whether the function y = is a solution of xy' +y cos x with the initial condition y(r) =…

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Q: (x²–1)dx S (x++3x² +1)[tan-1 x2-1 aluation of is

A: Given integral is I=∫x2-1x4+3x2+1tan-1x2+1xdx To evaluate I Now, dividing the numerator and…

Q: 57. Extension of Example 8 Show that cos (x) is dx sin (x). 180

A: The objective is to show that ddxcosx° is -π180sinx°. The function cosx° is given in degrees bu the…

Q: solving (2 x sinxy+x^2 ycos xy ) dx + X^3 cos x y dy = 0

A: given the expression is ; [xsin(xy)+x2ycos(xy) ] dx + x3cos(xy) dy =0

Q: sin x Evaluate: / dx (cos x) 3 1. tan x- sin x + c an'x + C X, sin'x + C X. 3. 2 4. log (cos2x) +c…

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Q: . Calc.   Test for exactness then solve. (2xy - sinx)dx + (x2 - cosy)dy =0

A: Differential equation

Q: f(x)=-7x(sin(x)+cos(x)) f’(pi/4)=?

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Q: log3 (2r² + y) + tan (2-³) = sin-¹ (²-1) +

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Q: et +e» et Рe-* cosh(x) sinh(x) 2

A: Given that:- coshx=ex+e-x2 sinh(x)=ex-e-x2

Q: (i) (x² + 1) tan-'x – x (ii) x³ loga x + e* cos x d (iii) e2 In cos 2x iv) 102 In cos 2x dx

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Q: sin x Check whether the function y = is a solution of xy' +y = cos x with the initial condition y(T)…

A: Function is y=sinxx and the differential equation is xy'+y=cosx. Differentiating y=sinxx with…

Q: 三 hp x so da -e" (sin x + cos x cos2 (x) sin x O)-e" (sin x C UIS e2x (p et (sin x cos x +66 acer

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Q: sin-1(e* 2 lim V1 - e2x x→0-

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Q: proof: -1 d du cot-1 dx 1 + u2 dx

A: Let cot-1u=t.  Therefore: u=cot t

Q: sin (), x + 0 10. Find the value of K which makes f (x) K, x = 0 continues at x = 0.

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Q: lim E(cos (27x;))Ar over [0,5] COS i=1

A: The definite integral is defined as  ∫abf(x)dx=limn→∞∑i=1nfxi*ΔxWhere, Δx=b-an, xi*=a+iΔx The…

Q: cosh-1 x dx CO: хах

A: Let the given integral be y - y = ∫cosh-1x dx y = ∫cosh-1x1 dxIntegrating by parts - y =…

Q: x' cos“ x sin x dx. (л- Злх + 3х Evaluate: | -

A: For the solution of the problem follow the next steps.

Q: e2x+Inx² sin x² dx -+fe²x cos x² dx

A: This is a problem related to integration. Based on the general formula we will solve the problem.

Q: P8: sin x cos x -dx J (2 sin x – 1)(sin x + 1)

A: ∫1au+bdu =1a lnau+b+C

Q: Cos(-) Q5. The value of indefinite integral 5x *dx using appropriate substitution is given by…

A: The given integral is ∫cos1x5x2dx.

Q: f(x) = 8 cos x- 8 sin x f'(x) = %3D

A: Given function is fx=8cosx-8sinx.

Q: ) Evaluate antan L tc 2 - arctan -x3 - 2 tc arctan 3- 2) Evaluate dx 5 arctan arctan x*-5 +C 45 -…

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Q: Explain why or why not Determine whether the following state-ments are true and give an explanation…

A: Since you have posted a question with multiple sub-parts, we will solve only first three sub-parts…

Q: sin(x) * x - lerror| < 0.0000001)

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Q: ∫ln a/x sin^-1x dx

A: Given,           I=∫ln(ax).sin-1(x) dx To solve this integration we apply integration by parts…

Q: The value of A. sin-¹ x +√1+ x² + C B. sin ¹x-√√1 + x² + C C. sin-¹ x + √1- x² + C D. sin¹x-√1- x² +…

A: The  given integral is ∫1-x1+x dx The trigonometric identity is expressed as sin2θ+cos2θ=1 therefore…

Q: f(x) = e-x (3.2 sin(x) - 0.5 cos(x))

A: Here a simple python script written follow that.

Q: Using FPI, find a critical point of the function: f(x) = x? – 2e* cos x With an initial guess, x, =…

A: Given function: fx=x2 - 2ex cos x Find the critical point of the given function Initial Guess:…

Q: X -dx 3. Using a suitable change of variables, determine the indefinite integral: √1 x² [ (sin² x)…

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Q: e-* cos² x (x + 1)2

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Q: sin x e dx Co x

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Q: . (sin a+ cos x) dy + cos x- sin x) de = 0. (Ans. y + log | sin x+ cos x|c)

A: Formulae used: ddxsinx=cosxddxcosx=-sinx∫1dx=x+c∫1xdx=log|x|+c

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.