8. S sin x(2 – 3cos x)²dx

Q: 2.Find if. y? +x? = sin(xy) using implicit derivation

A:

Q: If y=sin²r+ tant, x=- In(-cost) – e sinr, find the value of y' when = 6 2+ Vze VE 2/3 V2-e ? 2-Vze 2

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Q: 00 -dx- ;, 0 < p <1. sin px 7. Show that 1+x

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Q: The appropriate trigonometric substitution for * dx is V3x-x 3 3 X ==+ sin 0 2 2 sec 0 4 2 O Option…

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Q: (s,+)=(-3,1) X=5?+2+? y= 6st a) 4s x sinly) + 6+x?coscy) at (-3,1) b.) 8tx Sincy) + 6sx? Coscy> at…

A: GIVEN  (s,t)=(-3,1) X=s2+2t2  Y=6st substituting the value of s,t for X and Y we have  X=(-3)2…

Q: Eváluate the followng: pIn2e*cose*dx :/3 4 sin x dx 2- So rim 3- 2e*cose*dx 2- Jo x(Inx)- In 1-…

A: Given,

Q: Differentiate the following with respect to the variable: y = 5 In 3x Differentiate the following…

A: Given: 1 y=5ln3x2 y=3x2sin2x

Q: S tan ( – y) dy 4

A: ∫tany4-y dy=∫tany-4y4 dy=∫tan-3y4 dy Now put, -3y4=t⇒-341=dtdy⇒dy=-43dt

Q: Differentiate the following. Do Not Simplify. y=(sin x)(lnx) b) y = (e² + √√cos x) c) y = = a)…

A: To differentiate the following.a y=sin xln xb y=ex+cos x37c y=1-tan x3x3

Q: 04: S+* + 1)sin z dz =

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Q: Let f(x, y, z) = n(4xy) + sin(xy² + ye*). Find fayz.

A:

Q: sin x (cos x + 4) dx 1+cos?x

A: Solution:

Q: sin 4y w = y+1

A:

Q: Which of the following equations is equal to 1 A cosh (x) – sinh2(x) (B tanh²(x) – sech2(x) ©…

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Q: Simplify the equation: sechx + sinhx tanhx cosh z cosh a sechx 1+ sinh 2 cosh z

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Q: Solve for y cos>x + jsinycosy - sin?x = 0.866 + jo.5 (А) 15° В) 45° (© 15°, 195° D 45°, 225°

A: Using the properties of the trigonometric functions, it can be written that:…

Q: use implicit diff cos(xy) = 1 + sin(y)

A:

Q: 8) Find the dexivative of fex) - sinx cos x, Write your answer Single term. as a

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Q: Let x² + sin(yz) = xz² + y dz and ду dz Find

A: Given,           x2+sinyz=xz2+y

Q: If y=sin-t+ tant, xr= - In(-cost)-esinr, find the value of y when +VZe V? -Vzle 2 2/3 V2-e ?

A:

Q: QI: Find dy/dx for the following 1. y = (sin x + cos x) sec x 2. y 3. Y= (2 -x) tan2 x sinx+ cosx…

A: Product rule of differentiation:     ddx(f.g)=fg' + gf'

Q: dx Maybe used: sin(x – y) : 1. JTV#² + x + 1 sin a cos y – cos a sin y

A:

Q: Evaluate: cot[ sin! V212] O 2. O VZ 12

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Q: Evaluate and simplify y'. y = V1 - x* + x² sin-'x?

A: Given that y=1-x4+x2sin-1x2.

Q: True or false: V · (cosrŷ + Ve* – y°2) = 0. Explain why. r cos

A: Given that  ∇·excosxy^+ey2-y5z^=0 Now, ∇=∂∂xx^+∂∂yy^+∂∂zz^ So,…

Q: 2 x If y = x¯e" sinx,Find d

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Q: (b) 는(cosx)=-sinx (d) VI+ tan x 1+* Q1) Show that: (a) (1+x) =1+6x (e) (V): *- () %3D

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Q: If sinh I = 2 =, then tanh z is Select one: V5 O a. b. y5 2 O c. V5 O d.

A:

Q: sečxdx ztanx 5-9tarix ansi sin 2

A: Solution is done in step 2

Q: || dy tan(sin-lx) then find d.x 1. given, y

A: The given function is: y=tansin-1x To differentiate this function, apply the chain rule of the…

Q: Let x = 0.46 and y = 4.74. Determine the value of C when you ev |tan-(2x)dx.(Use 2 decimal digit)

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Q: 19. (cos x - sin x) dx = 2.828 4 20. (csc2 x) dx = 3.464

A: See the attachment

Q: 3. Sy sin 2x dxdy

A: we have to find integration

Q: State the trigonometric substitution appropriate to the integral: fx*(x² - 16)² dx 3/2 | A. x 16 sec…

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Q: 15. Evaluate Sin x cosx dx 2x Your answer 16. Evaluate se 3cos 2x Sin 2x dx Your answer

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Q: check by differentiation that y=5COSE 4 Sint is a solution to y"ty=D0 by finding the terms in the…

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Q: Use undetermined coefficients or annihilator y" + 25y = 6 sin 5x + x² %3D

A: To find the general solution of the given differential equation.

Q: Evaluate sin (x) cos(r)dx using an appropriate substitution.

A: Given that, I=∫absin5(x) cos(x) dx We have to find the solution of above integration.

Q: 1 17. Evaluate (4x? + 20* – 3e2x + + sinx)dx

A:

Q: The appropriate trigonometric substitution for dx is V3x-x2 ww 3 X = 9 3 + sec 0 2 4 3 +sine x = O…

A: We have to solve

Q: e cos(x) = 1 + sin(xy) 2 2

A:

Q: f sin x ln(cos x) dx

A: Our Aim is to evaluate the integral given below:-∫sin (x) ln cos x dx -(i)

Q: (x² cosh(sin(x – y) 8.

A: We have to find the partial differential with respect to x in question number

Q: Find the tangent of 2X. Х. 13 Y 12 Write your answer as an integer or as a decimal tan (X) %3D 5.

A: this is the right triangle

Q: 8. fx,y) = sinx cos y

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Q: Differentiate the following. Do Not Simplify. y=(sinx)(lnx)_ b) y=(e³+√cos x) c) y = º /1—tanx 3x³…

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Q: Evaluate ∫ex cos3(ex) dx using tables after performing the substitution u = ex.

A: We have to evaluate the integral by substitution method: ∫ex cos3ex dx Substituting, u=ex…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.