funetion:- sinty -X 1-COS X tank t cos X メ-secK X zo Dcontinous at Xz0 and equals Dcontinous at X=0 and equals-I 3 Not coutinuous A Not of the above

Q: f'uo) -22:2294 W = 0.4748 2nd Stetzation flui) = fla4748) = 31e flui)= 0.0044 f'ni)= flouT48) = -31e…

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Q: f'(x)= 3cos(x)+5sin(x), f(0) = 9 a. f(x)= – 3sin(x)– 4cos(x)+7 O b. f(x)=3sin(x)+4cos(x)+11 O c.…

A: Topic = Integration Correct answer  = C

Q: Derivatives: using (4 step rule). 1. q(t)=10 + 5t – 1? 2. s(x)= 3-x ,2 4. f(x)=sin3xcos 3x 5.…

A: Note :As per our guidelines we are supposed to answer only one question if there are multiple…

Q: 12. Find the first derivative of y = 2cos(2 + x?). A. -4x sin (2 + x²) B. 4x cos (2 + x*) C. x sin…

A: Since you have posted multiple questions. As par guidelines we"ll solve first question only. If you…

Q: sinh(3z+1) z2 - 5z+6 Evaluate dz, where C : |z– 2i|= 1, counterclockwise.

A: We have to evaluate ∮Csinh3z+1z2−5z+6dz, where C:z−2i=1, counterclockwise. Cauchy Goursat theorem:-…

Q: Secant method 3e-* -1 ACTIVITY #7: x² + 2x ; use interval [0,1] - cos?x

A: Given- x2 + 2x - 3e-x - 1cos2x; use interval 0, 1  To find- Find the root using the Secant Method

Q: ). y² = 4x, 2x - y = 12 ). y = In x³, y = In x, x = e ):y = 2sin x, y = sin x from x = – to x : %3D…

A: As per bartleby guidelines for more than one part only first part is to be answered , please upload…

Q: 7. Integrate: S sec? (n²x)dx A. 2n tan n² + C В. x sec2 п2 + С C.금tan(T2x) + C D. x sec nx + C 8.…

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Q: sin 3x 22. Integrate: JS dx V25-cos² 3x A. -sin-1 (os*) + C 'cos3x' (cos 3x` C. -sin *) + C 15 B.…

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Q: 12. Find the critical point y = x sin-x+ -x? %3D (1,0) O 1.-1) O (0,1)

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Q: sin 3y cot 5y Q7// Evaluate limy-0 y cot 4y

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Q: 3.44 3. Test for homogeneity f (x, y) tanx-sec²x - cosy

A: Question : Test for the homogeneity f(x, y) = tanx - sec²x - cosy

Q: 4 sin(x) cos(z) + 2 sin(z) – 2cos(z) – 1 = 0

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Q: 1 Eliminabe the arbitrary constants C,e"cos 2x - 3X SIn 2x + - ZX Y C,e

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Q: 9) f(x. v) = sin (x- 3y) Ans. f, =2sin(x-3y)cos(x-3y),. f, =-6sin(x - 3y)cos(x-3y)

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Q: Ave homerks anly -Sinx de Je esCaK-Cotax tany 6) X-1 Sook cos X-4 da Cos X f(onx-Sinede

A: As per company's guidelines, I can answer only one question. To know rest please repost the question…

Q: sinx+5* dy for y=In dx e3Xtan(x³) O a. Some other answer cosx+5*In5 3x²sec²(x³) - 3 tan(x³) b. dy dx…

A: We have given y=ln(sinx+5xe3xtan(x3)). Let us simplify right hand side using logarithmic…

Q: Using Variation of Parameters 4y''-4=cos-1x

A: Given that, 4y''-4=cos-1x Now let's take, 4y''-4=0 Take m=ddx, 4m2-4y=04m2-4=0m=±1 So the homogenous…

Q: cos(x) dx = dx. Use - 0o (1+x²)² o cos(x) 00 cos (x) Compute Jo 1+x²)² dx. Note that 2 (1+x2)2 the…

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Q: Q4 1-F(x)=limx→0 vV(x2+3)-3}/x2 2- limy 3y+5y2-7 10y3-11y+12 sin4x 3 - lim 0 sin2x

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Q: Exercise No. 2. Use Elimination of Constants by Isolation of Constants. Show your COMPLETE AND CLEAR…

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Q: tanx -√ S sec²x 1+ et tanx In (secx) √✓ 1+tan²x 1+ elanx sec ³x 1+etanx If f(x) = A B (с 1+1² 1+e'…

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Q: ation (1+xcos 2y)dr-x'sin 2 ydy = 0. %3D

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Q: 5. y + 4y = sin x + 3 cos x Ans: y = C₁ + C₂ cos 2x + C3 sin 2x + sinx-cosx

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Q: *y=(sin(x)+cos(x))cos(x). dyldx -sin 2(x)+cos*2(x)+2cos(x) -sin 2(x)+cos 2(x)-sin(2x) O

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Q: 4. sin 5. y = x ArcCC 1 + v1-x² 2+X 6. y = Arccot x + Arctan 1-2x >| ×

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Q: ♥ дzu ахбу = сезх созу, Ans: u(x,y) = sinx siny + x² + 2 cosy - #2² X 1 бу исx;#) =X бx U(x,п) =X,…

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Q: Q.3 Use ODE methods to solve the BVP: U = 18xy + sin(2x- y) U(0, y) = y -cos y, U(x,0) = x² -cos2x,…

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Q: 9. y= sin (r - (z+ 10. y = sin 4 11. y = cos (x – 4. (z + 12. y = coS 13. y = 1+ sin x 14. y = -1+…

A: Matching the graph of functions given by questions 10, 12 and 14

Q: Cos ly -A) %3D show that 2 ニ0 2 8x Sx8y

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Q: (1 + x²) dy + 2xydx = cot xdx y (1 + x²) – In|sin x| = C y (1 + x²) – In|cos x| = C y (1 + x²) +…

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Q: y sin 2x + cos 2y = ax Find y' a – y cos 2x y% = sin 2x – sin 2y а - 2у сos 2x y sin 2x – 2 sin 2y…

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Q: None c) cosh x + C sinh x +C 2 sinh x +C cosh x +C

A: The given integral,      12∫ex-e-xdx

Q: tan" -1 I# Z-X FEMD fyx At (-,1).

A: The solution for the above question is as shown below.

Q: 5. (cos" x- y cos x) dr - (1 + sin x) dy =0

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Q: QIN Evaulate : f v2 + cos4t sin4t dt

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Q: 5. у %3D е2*(с1 cos x + c2 sin x) 5. y = e2*(c1

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Q: sech x+csch x Q3: prove that e2x %3D csch x-sech x

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Q: solve eYsin(x) -y'cos"x = 0 2. cos¯x=0

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Q: sin x dy (1 + y) cos x + sin x If y=- , prove dx %3D cOS x 1+2y + cos x-sin x 1+ sin x 1+ 1+ cosx 8.…

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Q: 2ク • *ý-4xý +6y =-X sinx 3 2. Ans y= C,X +C2 X+X Ssinx

A: We have to find the solution of the give second order differential equation

Q: x1'=2x1 + 2x2 + t x2'=-x1 + 2x2 + sint  x1(0)=1 ve x2(0)=1 sistemini çözünüz

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Q: sin If y = , then justify (1–x² )n. -(2n +1)xy, – n² y,-1 =0 applying Leibnitz's a) theorem.

A: Please check step 2 for the solution.

Q: sin x dy (1 + y) cos x + sin x If y=- , prove dx %3| cos x 1+2y + cos x- sin x 1+ sin x 1+ 1+ coS x…

A: Introduction :

Q: 8) Prove: Prove that a general solution of the equation y" - y = 0 is given by y = c cosh t+cz…

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Q: Solution :- we have Fla) =5 cas 2x %3D Now di'fferentiate it wot x x d (cos2x) %3D Źx(-2sin2x) %3D…

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Q: S lim 1 (1+x)2+n³ cos (nº + x³) dr

A: HINT:  Used Integration formulas and limit formulas.

Q: Find the general solution of y''+ y =1/cos x

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.