Evaluate the given function tan²ydy = sin3 xdx is equal to.. 3(tany – y) 30 + cosx А. Зх - cos³x coSx 30 3(tany – y) В. Зх. cos?x | COSX CoSx 30 С. Зх - 3(tany - у) - cos³x cosx cos?x D.None of the Above

Q: The value of 1 cos (tan ¹y) + y sin (tan¯¹y) cot (sin¯¹y) + tan (sin¯¹y) is......... +y¹

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Q: a tan secy dy dx Jo Q2) a) Find b) Is cos4xv2 - sin4x dx = (2- sin4x) + C true or false? show me

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Q: Estimate the error if P 3(x) = x - (x^3/6) is used to estimate the value of sin x at x = 0.1.

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Q: 1 Differentiate y = tan 8x + cos ,x

A: Using differentiation rule,

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A: We will find the derivative of the given function in the following step.

Q: 26. i) differentiate, with respect to x a) cos (2Vx) In(2x) b) 27. Differentiate y with respect to x…

A: See the attachment

Q: Siny+ tany siny %3D 1+ secy

A: Let's find.

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A: Consider the function:  fx=2esinx2 The given function will be maximum when sin(x/2) =1 because the…

Q: „In sec²(sin2y)dy can be evaluated by writing it as sec2y A sec²(sin2y) - cos2ydy None © In…

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Q: Find Domain and Range бяц tue Ⓒsin (x+3) +2y x²+2y 3x + y² 3) 3x + Sin (3x) +2y+Z² Ⓒ x+2y cos2x…

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Q: 5. Find y', if y = 2cosx sin2x – sinx cos2x %3D

A: NOTE:according to company rules I need to solve first question when multiple questions are posted

Q: (b) Show that 1 2t and sin x = cos x= 1 +? 1 + ? (c) Show that dt 1 + f dx %3D 2.

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Q: (3) Estimate the error involved in using the approximation cos x = 1- for |x| < 0.01

A: To estimate the error involved in using the approximation cosx≈1-x22 for x≤0.01 The Taylor series…

Q: 9 If f(0) = cos 0 · cos 02 cos 03 ....... cos 0n %3D f'() + tan 0,}=- f (8)] Show, {tan 0, + tan 02…

A: Introduction :

Q: 3. Express 1++cos2x in terms of cos x. hence a. Evaluate (1+ cosx)dx b. Express 1- cos2x in terms of…

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Q: hich the extrema occur. g(x)=x^2+cos⁡(x^2 ) on [-√π,√π]

A: The function given is gx=x2+cosx2 on the interval [-√π,√π]. To find the extrema of the function…

Q: 5. Find y', if y 2cosx sin2x – sinx cos2x %3D

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Q: ayfor gen f(x) = cos (2r + (/2)), a = /4 TT

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Q: If f(x) Files = Time left 0:5 sin²x and g(x) = 1 + cos²x, how are f'(x) and g'(x) related? Maximum…

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Q: 2. The suitable Trignometric substitution that solves fx(x-2) dx is (x-1)=sin 0 x-1)3sec0 (x-1)=tan…

A: We can find the answer as below.

Q: 3pi

A: 1.Cos(x-y)=Cosx*Cosy+Sinx*Siny 2.Sin(x+y)=Sinx*Cosy+Cosx*Siny In a right angled triangle, 3.Sin X =…

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A: We can solve the given problem as follows:

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Q: Find the value of parameters € and ¶ that makes f(x)=€x+¶ if x&lt;0 and f(x) =2(¶+€)sin(x) +…

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Q: > fnd period of 8- tan 4x 10 2 y. 5 Cos 10* 11 12 → Skekch these funchion 3- 13 14 1 ys 3Sin (X +T)…

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Q: šx<2a . dation where 1 1. sin x = 2 2. 3tanx-1=0 3. 2cosx=cosx

A: We will find the values.

Q: Find for the following functions: (4) y = x sinh 2x --cosh 2x (2) y = tan³√/cot(7x); (3) y= sin Imvr

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Q: Find the general solution of the differantial equation given by www |y" – 4y' + 5y = 3xe* – cos2x +…

A: Given y''-4y'+5y=3xex-cos2x+x+1sin2x

Q: 6. Evaluate |2 Sin xʻdx, by (i) mid-point rule, and (ii) Simpson's 1/3 rule.

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Q: 1 what are possible values of cos x and tanx? 2 If sinx= Select one: V3 and tanx= 2 1 a. cosx= V3 V3…

A: Consider the right triangle with one angle x degree. Let a be the length of the adjacent side and b…

Q: Evaluate: | sech[In cosx]tanx dx A -2 tan -1(e cosx) +C В -2 tan -1(cosx) +C 2 tan -(ecosx) + C (D 2…

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Q: Determine an equation for the sinusoidal function shown. 2. 12 21 Oy = 0.5 cos[0.5(x+ x)] + 1.5 Oy,…

A: The general equation of a sin function is given by; y=A cos(Bx+C)+D Where; A→Amplitude of the…

Q: 9. Evaluate y' of y = e-2*sin3x a. 3e-cos3x- 2y b. 3e-cos3x- 3y c. 3ecos3x - y d. 3e-cos3x +y e. Not…

A: Explanation of the answer is as follows

Q: 10. Solve for t on the interval [0, 2π) (a) 2 cos² t-cost-1=0 (b) 2 sin²t-3 sint + 1 = 0 taol al (c)…

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Q: 1. f cos³ 3x sin¹ 3x dx 2. fcsc4 5x cot4 5x dx 3. ƒ cos³ xdx from a = 0 to b = 2

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Q: Differentiate D = x2 + sin25x with respect to t and simplify. x2 + sin? 5x dt dt x2 + sin2 5x)1/2 dt…

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Q: 2. Find the linear approximation to hly)=sin(y+1) at y=0. Use the inear approximation to approximate…

A: linear approximation.

Q: 3 Find cos(x+y), given that cosx= and siny = 2 3 TT <y<2n. 0<x< 2 Select one: V5-2/15 a. 10 b. None…

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Q: 9 If f(0) = cos 01 ·cos 02·cos 03 ....cos 0n %3D Show, {tan 0 + tan 02 + tan 03 + ... + tan 0,}=- f…

A: First note the results derivative of log x is 1x and derivative of cos(x) is -sin(x). The proof of…

Q: Obtain the GENERAL SOLUTION tan'ydy = sin xdx xdx-Sa²-x² dy =0 y'exyz

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Q: 3 Q19- if z =- 4x³y sin sin (x³y) əz find əx

A: We want to find partial derivative of the given function.

Q: 5. Find the slope of the graph of cos(x + y) = 2x at the point ( 0, n/2 ). Hint: Differentiate…

A: Dear,as per company guidelines we can answer only one question at a time, kindly post other question…

Q: Particular Intecral for the differen tial equation (0+0ly=Sin k is given by . * COSX * Sinx Sinx D0.…

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Q: 3. y³x2 – cos- sin x² + esin x = 1 y DIFFERENTIATE THE GIVEN

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Q: Consider the following IVP: y" + y' = -cos x; y(0) = a, y'(0) = b Find the general solution. A y(x)…

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Q: 3 Differentiate: y = In cosh° (cos 2x)

A: As we know that: The chain rule: fgx'=f'gx·g'x The Power law: ddxxn=nxn-1 From the given problem:…

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.