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Q: Find the indefinite integral: 10sin 3x - 15 cos 2x + 6 e5x + C O 90sin 3x -60 cos 2x + 150 e5x + C…

A: 30∫cos3x+sin2x+e5xdx=30· ∫cos3xdx+∫sin2xdx+∫ e5xdx=30·…

Q: If n = 18, then the interval of the form (- t(n-1), alpha/2 , t(n-1), alpha/2), that contains 99% of…

A: From the given information, number of observations n = 18. Confidence level  Level of significance

Q: Compute 3 In(x² + 1)dx=

A:

Q: Find of z = In(xy)

A: Given,Z=ln(xy)differentiating both the sides partially w.r.t. x∂z∂x=1xyy1∂z∂x=1xagain differntiating…

Q: @) 2) Fs of (x) = -PFC (Psy) -} [ If f (x,y) → as 6004X proof. (H-w.) then в

A: Introduction: The Fourier sine and cosine transforms are variations of the Fourier rework that do…

Q: Evaluate the indefinite integral S(z -9-dz 를-9z + 듣 +C 4x4 중-9z + + C 222 - 9x + 7lnx³ + C - 7 9x -…

A: First we write each term using exponent

Q: 1. Show that cosh 4x = 8cosh“x - 8cosh? x + 1 .

A: Given problem:- Show that cosh(4x) = 8cosh4x - 8cosh2x + 1

Q: Find the indefinite integral: O 10sin 3x - 20 cos 2x +6 e5x + C 90sin 3x 60 cos 2x + 150 e5x + C…

A: The objective is to find the indefinite integral.

Q: 2. Show that X H→ In x is increasing on (0,0) and that In 1 = 0:

A:

Q: Exercise: 1.Find the interval and radius of conv. of In(1 – x?) ?

A: As per our norms we are allowed to solve one question at a time. Kindly repost the rest question…

Q: Prove that Cosh [m(t-x) Cosh mh 2mL 2mL

A: The given data is: To prove: emx1+e2mL+e-mx1+e-2mL=coshmL-xcoshmL

Q: Compute integral-11  3x -√1-x^2  dx

A:

Q: Evaluate the integral. x3- 2x2 - 4 dx x3 - 2x2

A:

Q: The first derivative of the power series 9 9x2 9x3 9x4 f(x)=9+ .. is 1! 2! 3! 4! O -9 f(x) O f(x)…

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Q: Inn NTT <os 2. n=1

A:

Q: Differentiate y = laz az-1 In r Option 2 None of these 2n In z Option 3 Option 1 2ln-1 In z

A:

Q: 6. Prove that 1 cosh(tanhx) : -1 <x < 1. V1- 12

A:

Q: LV3x2 - 2x + 3 (3x – 1)dx

A:

Q: Evaluate the definite integral. '1 3 + 7t³j+ Vik) dt /-1

A: Consider the given definite integral

Q: Еxercise 13 Determine how тany times 0 арpears in thе тultiplicatioп table for Z16-

A:

Q: 6) Prove mathematically that (1 grad = 0.9 deg) %3D

A: Since, this is a multiple question according to the Bartleby Answering rule, only first question is…

Q: Evaluate the integral: Sen(1²2+3x-7) е dx A x² + 5x+In 3x-6|+C XZ B +5x+31n|x-2|+C 2 C x ²2+ = +…

A: On solving this we will get

Q: Prove that In (1tx) Lx for without using the value the orem. mean

A:

Q: Evaluate the integral∫ (4 /√(4 - x2)dx.

A: Let, I=∫44-x2dx Substitute x=2sint  gives dx=2cost dt…

Q: Prove using the IVT. ex + In x = 0 has a solution.

A: IVT: If f is continuous on the closed interval [a, b], f(a) ≠ f(b) and k is any number between f(a)…

Q: on inteaurron (ii) Determine the general formula for V Pn.

A: Numerical analysis.

Q: 2. Estimate V50 using tools from calculus.

A:

Q: 9 In(z² – 1) dz

A: Given: ∫9lnx2-1dx

Q: Show that L₁J - dx x² + 2x + 2 = In(√5-2).

A:

Q: Evaluate the integral. 8. (x³ - 6x) dx -8

A:

Q: Use any method to evaluate the integral. 8× – 8 -x -dx 8* +8-*

A: To evaluate the integral

Q: 6(2tanx - x^4 + 4lnx)^1/4(2sec^2x - 4x^3 +4/x)dx. Hint: let u = 2 tanx - x^4 + 4lnx

A:

Q: 1. Express into parital fraction. Hence evaluate y2 -4 *2-4

A: according to our guidelines we can answer only three subparts, or question and rest can be…

Q: Proved that cosh fas/ (cashZ+L)

A: To prove :  cosh2z2 = 12cosh (z) + 1

Q: 2. Estimate the root of the expression, f (x) = 8 – 4.5(x – sin x), using False-Position Method in…

A: Here f(x)=8-4.5⋅(x-sin(x)) 1st iteration :Here f(2)=3.091838&gt;0 and f(3)=-4.86496&lt;0∴ Now, Root…

Q: None of These cosh(4t) 7. 2. 7. - sinh( 21) sinh(4t) 7. cosh(21) 7. Sて 1/2 1/2 1/2 1/2

A:

Q: 4. Letf(x)=x22/5 - 19x². Determine the largest n for which fis n-times continuously differentiable.

A:

Q: 1.Find the interval and radius of conv. of In(1 - x2) ?

A: Maclurin series representation for ln(1- x2 ) is  ∑n=0∞-(x)2n +2n+1   (Why?) Explanation As ln(1+x)…

Q: 2. Determine the positive real root of the function f(x) = In(x²) – 2 with initial guess [5/2, 3]…

A:

Q: Evaluate the integral x³ - 3– 2x2 - 4 dx x3 -2x2

A: We have to find integration in this question.

Q: Find the interval and radius of conv. of In(1 – x²)

A: The power series representation of given function ln1-x2 is given by: ln1-x2=∑n=1∞-x2nn

Q: 38 Show that x² V2x – 3 dx - 35

A: use the formula below to evaluate the given integral.

Q: The integration expression sin(3In(x)+ 4)cos(3ln(x) + 4)dx must be transformed into using suitable…

A:

Q: Choose the most appropriate answer: Evaluate the integral : S(19 Inx) dt O 38(2 ln 2 + 1) o 19(2 ln…

A: The integral is ∫12(19 ln x)dx

Q: Evaluate the integral. 3. [(ax-2-4) dx 2.

A: The given integral,        ∫234x-2-4dx

Q: 3-Expand In [x? sin³ x /vx2 +1]

A:

Q: Prove that 1- cosh -1 x= In(x+ Vx- -1 1 x+1 2- coth -In x-1 X = - Vi+x? .2 1 3- csch -1 x = In(-+

A:

Q: eturns ABC XYZ 0.2515 -0.22 55 0.4322 -0.28 45 -0.14 33 0.3144 -0.0645 -0.51 14 0.33 78 0.5534 0.68…

A: Covariance and correlation are two important concepts in financial analysis.