Show that y = -cosx In(secx + tanx) is a solution of y" +y = tanx

Q: Separate tanh-1(x+ iy) into real and imaginary parts.

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Q: Find the linearization of ƒ(x) = √(x + 1) + sin x at x = 0. How is it related to the individual…

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Q: Describe the method used to integrate sin" x cos" x, for m even and n odd.

A: The method to integrate sinm x cosn x when m is even and n is odd. We integrate by substituting the…

Q: Find integral.

A: Given: Let I=∫2x cos x2 dx To Find: To evaluate the given integration.

Q: Determine of y = cos(x) – V5a2 In x.

A: I have stated the used formulas in the solution.

Q: Solve using Substitution Method. y(x Tan x + In y)dx + Tan x dy 0

A: The substitution method as follows, y (x tanx + ln y) dx + tanx dy = 0

Q: Differentiate: y = sinh° (sin 5x) Oy' = 15 cos 5x sinh (sin 5x) cosh(sin 5x) Oy' = –15 sin 5x sinh?…

A: dsinh (ax)dx=a cosh (ax) dsin(ax)dx=a.cos(ax)

Q: If Sin-'x= Iny, show %3D ( l-xx) day - dx d X 2 x dy =y

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Q: Differentiate : a. y= x^2 sinx +sin^2x + cos^2x + tan 2x/sin2x/cos2x b. y= In √x^3

A: a) y=x2sinx+sin2x+cos2x+tan2xsin2xcos2xb) y=lnx3

Q: what is the antiderivative of   (sinx/1+cos2x) dx?

A: Let,

Q: Differentiate : a. y= 9x sec (x/3) b. y= sin2x/1-cos2x

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Q: x sin 2x sin cos x 2 Prove that: dx = 2x- T

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Q: find integral tan 3 x dx

A: To find the integral of tan2x first split tan into two part and the using property of sec and tan…

Q: derive ^x dx cos"x Sinx + n-1 Cash Cos"-2x dx n-2, X. Jos"x dx in

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Q: x/2 | (cos(x) + sin(2x)) dx of

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Q: 11. Integrate. a. x3 b. S(5 tan 3x – 2 sec2 x)dx

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Q: 9.) JE sin°(x)cos*(x)dx 11.) F sin°(x)cos²(x)dx 2

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Bind dy, 4. Ssinx.cosx sinx-coSX 1 +2.Ln X

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Q: Differentiate y = coS 7 + sin4x+ x cos x + 4 with respect to x. 1. 2.

A: the given function is: y=cosπ+sin-1(4x)+xcos(x)+4x3 we have to differentiate the given function with…

Q: f y=sin(sinx) show that y'' +(tanx) y''+y cos2x=

A: Given that y=sinsinx To show that y''+tanxy'+ycos2x=0

Q: Evaluate: S Arctan 2 sin²x dx . Arctan 1 cos+x

A: Given,  ∫Arctan1Arctan2sin2xcos4xdx

Q: Find the solution of (tan x – sin æsiny) dæ +cos xcosydy = 0

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Q: (b) Show that 2t cos x and sin x = 1 + ? (c) Show that dt dx 1 +

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Q: solve for the intergral of (2sinx)/(1+cos^2x)dx

A: The integral to be evaluated is  ∫2 sinx1+cos2xdx. Here, we can use substitution method to evaluate…

Q: y" + 2y' = sin 2x ||

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Q: 2. if 2x3 +10 x?siny-y"tanx = 0 ノ the y' so dy write ex pressin in terms of X and y.

A: Applying implicit derivative we have

Q: Show that bothy= sinx and y = cos x satisfy y" = -y

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Apply variation of parameters to find a particular solution of y ''' - y' = tan x

A: The given differential equation is y''-y' = tan x.We have to solve this using the variation of…

Q: The first derivative of y = sin( 4x + 3) is %3D а. - 4 cos(4x +3) b. 4 cos(4x +3) С. cos(4x+3) d. -…

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Q: Describe the method used to integrate sinm x cosn x, for m even and n odd.

A: Method to integrate sinmx cosnx ,for m even and n odd. Let m=2k and n=2k+1 ∫sinmxcosnx…

Q: Differentiate: y = ln cosh (cos 2x) 3. O y = 6 sin 2x tanh(cos 2x) %3D O y = 6 sin 2x coth(cos 2x)…

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Q: Differentiate y = coS 7 + sin4x+ x cos x + 4 with respect to x. 1.

A: 1) The given equation is y=cosπ+sin-14x+xcosx+4x3 To find: dydx

Q: 19. i) Differentiate sinx with respect to x from first principle 1+3x dy ii) Find, dx when a) y (x…

A: Part i,Given,          fx=sinx

Q: First and second derrivative of: y=5 /(sin 3x+cos3x)

A: the given function is: y=5sin3x+cos3x we have to find the first and second derivative of the given…

Q: 57 ves y sinx and y=cosx from x=- to x=- 4 4

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Q: S tanʼx dx

A: Answer is given in next step.

Q: ind the equation of the line that is tangent to y = 2x + sin x + cos x at x = 0.

A: NOTE: Refresh your page if you can't see any equations. . take x=0 the point on the graph is

Q: The second derivative y" of y = x3 + ex – sin(2x) is . 1. O y" = 6x + eX – 8 sin(2x) 2. O y" = 3x +…

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Q: Show: 2 x + 2 sin dydx + 2y 1 va sin-dydx = 4 2y 2 va

A: The question is of change of order. First we need to identify the region formed by limits of…

Q: Left in implicit form

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Q: 3T 2cosx dx 1+(sinx)2 2 a)2 tan-'sinx|| b) 2 In sinx| c)2 In(1 + (sinx)² 2

A: We know that integration of 1/(a2+x2) is (1/a) tan-1(x/a) +c. Here' c 'is constant. Here i attached…

Q: Integrate by parts f(x)=sin4(x)cos3 (x) dx

A: Given the integral  I = ∫cos3(x) sin4(x) dx cos2(x)=1−sin2(x) I = =∫cos(x)(−sin4(x)(sin2(x)−1)) dx…

Q: In (sinh x ), + tanh x j + 1-x k )dx 1- sinx

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Q: Show that Sx cos*x dx = (x² + x sin 2x +cos 2x) + c

A: Given: ∫xcos2x dx=14x2+xsin2x+12cos2x+C.

Q: x sin 2x sin cos x 2 X. Prove that 8 dx 2х - л

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Q: Differentiate implicitly for the equation for x^2y+x^3-cos(x)=3y^2

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Q: If f(x) = A B tanx 1+e 1+1² 1+e¹ In (secx) √ 1+tan²x 1+ e tanx sec 3x tanx -dt, then f'(x) equals

A: solution:-f(x)=∫0tanx1+t21+etdtApplying leibniz integral…

Q: find tan x dx x² x² tan¬' x dx 19. 20. sin 3x cos 2x dx 22. sin 2x cos 3x dx S sin sin 8 sin 4t sin…

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Q: Verify that sin(x+y)+sin(x-y)=2sinxcosy

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Q: Q4) Prove that dx 1+ 2 sinx || In √3 Χ tan tan x + 2 -√√3 +2 + √√3

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