Find a series of cosines of multiples of x which will represent (x sinx ) in the interval (O, x) and show that: 1 1 1 п — 2 %3D 1.3 3.5 5.7 4

Q: Given that cos(x) = (-1x2 for e<xc than a powr saries of cas(x) %3D ie e (2n)!

A:

Q: Find the correct estimation of the value tan-1(2) by using Simpson's Rule with n = 4. A.) 1.1384 B.)…

A: Simpson's 1/3 rule ∫abf(x)dx≈h3(f(x0)+4f(x1)+2f(x2)+4f(x3)+2f(x3)+ ⋯ ⋯…

Q: Determine how large the number a has to be so that dx

A: To solve this problem we will first solve the integration and then use the concept of linear…

Q: 3 Given that 3. e dx = e° - e, use this result to evaluate 3ex + 4 dx.

A:

Q: If f(x) is odd and ∫-1 to 5 f(x)dx=11 then, ∫1 to 5 f(x)dx=?

A: It is given that f(x) is odd and

Q: Let P be an approximation of pai accurate to n decimals. Show that P + sin P gives an approximation…

A: Substitute the value of P in |f(x)|.

Q: Find for the following function. xp y= 3x cos x sin x dx

A: Given the functiony=3x2cosxsinx

Q: Estimate o cos(x2) dx using (a) the Trapezoidal Rule and (b) the Midpoint Rule, each with n = 4.…

A: Given: ∫01cosx2dx To Estimate: The given integral usinga. Trapezoidal Ruleb. Midpoint Rule

Q: Given a function f(x,y,z) = (x+7) In (6y - 4) sin (1z). Find the range of the function.

A:

Q: Evaluate the following 1. S sin x sin (cos x) dx

A:

Q: find x for which = 0. dx

A:

Q: Integrate the following. 3. f sec?x dx tanx

A:

Q: If f(s)=sinh(s)^13 cosh(s)^10 , find f'(s)=???

A: We have  f(s)=sinh13(s)*cosh10(s)   We have to find its derivative…

Q: Find the length of the graph of f(x) = In(4 sec(x)) for 0 < x <. %3D a) O1/4 In(3) b) 03/4 In(3) c)…

A:

Q: Prove the left side equal to right side in the following: s2 (eice = (sin at + at cos ar] 1 L-1 (s²…

A:

Q: . Use the trapezium rule to estimate the value of the following correct to four decimal places a)…

A:

Q: The following table shows corresponding values of x and y for | x² sin dx 5л 2л 4 9.870 14.207…

A: This question is related to integration.

Q: Use at least 6 decimal places of accuracy 1. C sin (z² + 2) dx using n = 6 2. √ √² +6dz √² +6 dz…

A:

Q: Which of the following is equivalent to / Isin(Inx?)]²dx , sin(Inx 14) dx A sin2(Inx 14) dx O (sin…

A: Given that, The given integration is following, I=∫[sin(lnx7)]2dxx We have to find the equivalent of…

Q: Calculate MN and TN for the value of N indicated.

A: Solution Given∫0π2sinxdx   , N=6we need to find the MN and TN for the value of N indicated.

Q: Find the root of the function ((x) =sin x -e in the interval (0,1) using the formula g(x) =aresin…

A:

Q: From the equation, f(θ)=sinθcos2θ-(cot θ / θ) +1, what is/are the critical points?

A: Consider the equation

Q: The approximation of I = , tanx dx using composite Simpson's rule with n-5 is: None of the choices O…

A: f(x) = tanx Each interval h=(b-a)/n =1-0/5=1/5 =0.2 xO=0, x1 =1/5, x2=2/5, x3=3/5,x4=4/5, x5=1…

Q: calculate MN and TN for the value of N indicated.

A:

Q: e cos xy [ydx + (x + tan xy) dy] = 0 %3D

A:

Q: Suppose the voltage in an electrical circuit varies with time according to the formula V(t) = 90…

A:

Q: S car'x dx cos

A: To find: The value of ∫cos4x·dx. Given: The integration is ∫cosnx·dx=sin x·cosn-1xn+n-1n∫cosn-2x·dx…

Q: Compute the following. S3x?cos(x³)dx

A:

Q: Find the egetion of the tanqent line on the interval (o,5) to co.1, 6.2)

A:

Q: Given f(x,y,z) = sin (2xy) + 5xyz3. Find fyzy(3,2,4).

A:

Q: When evaluated, | x sinh 3x² dx is equal to A. cosh3x? +C B. cosh3x? +C C. 3 cosh3x? +C D. 6 cosh3x…

A: we will let  3x2= t  to solve this question.

Q: The integral S (A S- (в x dx x² + √√√x²-1- sino do 1 + cos sec²0 do 1+tano " cose de 1-sino sece…

A: Use trigonometric substitution

Q: Use D'Alembert's formula to solve the following (IVP): Utt in R x (0, 0) | u(x, 0) u(x,0) = sin (x)…

A:

Q: Which of the following is a multivariate function? No answer 5e-sin z cos (e) e V2x? – y

A:

Q: Given the integral secº (x - 1) tan* (x − 1)dx, which of the following equations will be useful for…

A:

Q: The value of cos jn is equal to O a. sinh 7 O b. jcosh 7 Oc jsinh 7 O d. cosh 7

A:

Q: Q6) Calculate the mean value of y= 24 sin5 0 cos 0 from 0 = 0 to 0= J\6

A: Mean value is evaluated.

Q: Solve for sin(z) cos(z) — sin(z) = 0, when 0 ≤ ≤ ≤ T. z a) x = 0, π, F. 5 O b) x = 0, п O c) x =…

A: Topic:- trigonometry

Q: Given f(x) = sin(5x + ) a) Use P3(x) to approximate f () b) Use Lagrange error bound to show S ()-…

A: (a) The Taylor's series of sin(x) is as follows: sin(x)=x-x33!+x55!-x77!+x99!-⋯ So, we get…

Q: . Determine how large the number a has to be so that dx

A:

Q: Determine how large the number a has to be so that 00 dx

A: Given, ∫a∞1x2+1dx&lt;0.009

Q: (a) Use the definitions above to show that d tanh x dr 1 cosh r

A:

Q: suppose the voltage in an electrical circuit varies with time according to the formula V(t) = 60…

A:

Q: The approximation of I = tanx dx using composite Simpson's rule with n-5 is: O 0.6158 0.6165 None of…

A:

Q: Find all values of x on the interval L0,27) that ssue the following equabion coslex) +sin(n) -l=0

A:

Q: Given a function f(x,y,z) = (x+6) In (5y - 5) sin (9z). Find the range of the function. %3D

A: For the solution of the problem follow the next step.

Q: Find the value of b so that (2x – 1)dx = 10 O 1 O 4 O 2 3

A:

Q: Given f(x) = 3 sin x cos x, find f prime (x)

A: Derivative problem.....

Q: Mclopens serial f(x) = cos x she ?

A: Given function is f(x)=cosx

Q: Determine the percent relative error based on trapezoidal rule, with n =4 -5 2.5 sin(1.5 x) + 1.22…

A:

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.