QUESTION 16 f'(z) dz I2|=4 f (z) If f (z)= By Argument principle Find (z-1) (z - 2) 2 Ti None - i - 2 Ti

Q: sin 3x cos 3x (cos 3x + 1)² dx 19) f 22) fex√3-4e2x dx 20) f ITV In x dx 21) f x√4 lnx-1 23)…

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

Q: 1. Interval, 0 < x < 2; function, f(x) 0 < x < 1, 1 < x < 2. = 2 – x, 4 1 ANS. f(x) 1 +* E 2 cos – 1…

A: Fourier Cosine series expansion of the function

Q: Differentiation#11

A: We have

Q: { 1/(x + 2) , x2, sin(x – 1)/(x – 1), x 1. y = F(x) : %3D - 2- -1 3. 6. -2- -4- -6- -8- ounan a n…

A: y=Fx=1/x+2,        x&lt;−2x2,                  −2≤x≤1sinx−1/x−1,  x&gt;1

Q: 1. f(t) = cos*t – sin*t 5. f(x) = tan 2x 1-cot 2x 2. y= sec20 – tan²0 3. f(x) = sin(cos x) %3D 3 4.…

A: Here we have to find derivative of given questions.

Q: * (D'+1)y(x) = tan(x) 1-sin(x) 1+sin(x) 1+cos(x) - y,(x) = sin(x)In m(x)s03 = (x) 2- -- y,(x) =…

A:

Q: 4. Find (f-1)'(1) if f(x)=x' +8x+sin(3.x) а. Find (f-1)'(2) if f(x)= Vx' +x +xr+1 b.

A: To find the derivative of the inverse of a function

Q: 1. f(x) = sin 2x + cos 3x + x² = 0 with xo = -0.5 , Ax 0.1, TOL = 0.001, in [-0.5,1] %3D

A: Given equation is fx=0 where f(x) is defined by fx=sin2x+cos3x+x2  Given initial solution is x0=-0.5…

Q: Sx' cos(x4) dx = o 1 cos(x*) + c 4 - -1 - cos(x*)+ c 4 1 sin(x*) + c 4 -1 sin(x*) + c 4

A: *concept :- let, x^4 = t then integrate the simplified term cos(t).

Q: #35

A: 35) to differentiate the given function

Q: 27. f"(1) = 12 + sin 1 28. f"(t) 29. f'(x) = 1 + 3x, f(4) = 25 30. f'(x) = 5x- 3x? + 4, f(-1) = 2…

A:

Q: 7. F(t) = [sin (t -) - cos (t -)u (t -) | 8. F(t) = 8 sin cos t 9. F(t) = cos cos (; – bt) - bt), b…

A:

Q: sin 2x + 2 5я 3 + n, 3 5я + 2 n, + 2 яп 3 3 5я + KN, 6 2 я ○쓸+2.0, + 2 n 6 3

A:

Q: Increasing and decreasing functions Find the intervals onwhich f is increasing and decreasing.

A: We'll answer the first question only since the exact one wasn't specified. Please submit a new…

Q: [10 sin(2x) cos(2x) √ cos²(2x)-5 dx O a. 5 (cos² (2x)-5) ³/5 + C 3 5 O b. -(cos² (2x)-5)³/2 + C OC.…

A: To evaluate the given integral.

Q: 9. If f (x) = sin 3x so lim f(x+2h)+f(x-2h)-2f(x) ... -18h2 А. —3 sin 3x В. —2 sin 3x C. sin 3x D. 2…

A:

Q: •tanx √1+1² 0 1+e' sec ³x 1+etanx If f(x) = A B C D -dt, then f'(x) equals 1+tan²x 1+e' tan.x In…

A: Solved below

Q: Leb Fur =ue Show thab f6/0 )c

A:

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

A: As per our guidelines we are suppose to solve only first question. Kindly repost the other question…

Q: sin(4x) cos(2x) dx = cos (2x) cos (6x)' sin (2x) cos (2x) сов (10х) 4. (2x) sin (10x)+ c sin +c 10…

A: Use formula 2sinAcosB=sin(A+B)+sin(A-B)

Q: 1. If tan-1 x x 1’ f(x) = Then S(x) dx =?

A: This question is related to definite integration, We will solve it using given information.

Q: 1) Find All solutions For y = 3.0 to the Transcendental equation: sinx-ln z = X - Y + gamma x This…

A: note : we will refer the term "gamma" at the end of the  equation as the symbolical constant : γ =…

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: ,x € (0, 2] ,a = 0 f(x) = sinx then f (x) dx = 1 3 2.

A:

Q: 4.4. Show that the function f(x) = Sx² cos 1, if x = 0, ૨૦. if x = 0 is a BV-function over the…

A:

Q: Find the iterative scheme for the root of equation sin x-3x +1=0 by Newton-Raphson method. O a. None…

A:

Q: (§5.4, Q42) Calculate So™ f(x) dx, where sin x, x T

A:

Q: sin(6x) cos(4x) dx = sin (2x) sin (6x) (b) 글(s сов (2х) cos (6x) 2 o+( cos (2x) cos (10x) sin (2x)…

A:

Q: SV1+ sin2(x - 2). sin (x – 2). cos (x – 2) dx

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: 71. Prove the reduction formula tank x dx = tan" k-1 х | tank-2 x dx k – 1 Hint: tank x = (sec² x –…

A:

Q: x*sin (2x) dx a. ** cos(2x) – x³ sin(2x) –r² co. 3 x² cos(2x) +x sin(2x) +- cos(2x) + C 4 1 cos(2x)…

A:

Q: 4) f(x)= cos x COS X %3D (5) f(x)=xsinx -1+ Cos nx

A: Since you post more than one question. As per our guideline we can solve only first question for…

Q: If  f(x,y,z)=ln(x2y+sin2(x+y))+227x228y2z229,  then    ∂4f ∂x2∂y∂z at (1,1,1)  is equal to

A: See the attachment.

Q: 6. f(t)=-e" sin (2r + 7) -2t 7. f(1)= 3e " cosh (In 21) %3D

A:

Q: •5 6- Let f(x)dx = 10, f(x)dx = 9, f f(x)dx = 2. Find f(x)dx and (10f(x) – 9)dx =

A:

Q: 11. y = x² sin x + 2x cos x – 2 sin x 12. y = x² cos x 2x sin x – 2 cos x - -

A:

Q: Briefly discuss the origin/history of De Moivre's Theorem.

A:

Q: 2. Let f(x) = -x³ - cosx and po = -1. Use Newton's method to find p2. Could po = 0 be used?

A:

Q: 7.2 (A) 1. S sin x dx cos x + C because(-cos x +C) = %3D dx 2. S cos x dx = because sin x 3. S tan x…

A: We need to solve the given integral. This can be done as follows:

Q: [² 11. [(2 sinx+cos.x) dx 9. 13. 15. x¹/3 19. 21. 3 x2/3 - dx 17. [(3 cos x - 2) dx [(5x- 2²/1) dx…

A: Disclaimer:  “Since you have asked multiple questions, we will solve the first question for you. If…

Q: Z {sin(3t + 2)} O (5 sin (3) + 2cos (3))/ (s^2 + 4) O (s sin (3) + 2cos (3))/ (s^2 + 4) (s sin (2) +…

A:

Q: f(x) = tan (2x5 – x) %3D f'(x) = 9хcosx f(x) = %3D csc(x) f'(x) = %3D f(x) = ex f'(x) = %3D e5x+3 y…

A:

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: 17. Evaluate f-3x cos 2x dx a. --cos 2x - 3xsin 2x + C b. -cos 2x -sin 2x + C C. -cos 2x -³x sin 3x…

A:

Q: 6. x sec x tan x dx

A: Let's find.

Q: Why does Newton’s Method fail when f′(xn) = 0? What does this mean graphically?

A:

Q: 5-7 -1 Using quotient rule, show-that d [cotx] dx 2. 1+x

A:

Q: solve it 1- cos x 37. 1+ cos x 3 38. sin x = cos 2x 39. tan'x + tan?x – 3 tan x – 3 = 0 40. cos 2x…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

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.