find do diy y = (cos(x))*os)

Q: 1 2 de 4-cose %3D II

A: Given,          ∫0π214-cosθdθ

Q: Integrate -- | cos 5xcos x a) 0.5 b) c) d) 2

A: We can use the trigonometric identity, cos A cos B=12cosA+B+cosA-B . Use the integration formulas,…

Q: 2 lim In (cos x)e

A:

Q: Find integral.

A: Given: Let I=∫2x cos x2 dx To Find: To evaluate the given integration.

Q: 2. Find an interval where f,(x) = sin2 x and f2(x) = cos² x are linearly independent. %3D

A: W(π/4) = -sin(π/2) = -1 W(π/6) = -sin(π/3) = - √3/2 Since, Wronskian is not zero for a single value…

Q: Differentiate. y =  emx Cos nx

A:

Q: ) Evaluate A) /16 /2 cos (167 x5 ) dx dy. Os xs 2 Og y s x*

A:

Q: Obtain general solution   y¹ = cos²x cos y

A: Obtain general solution  y¹ = cos²x cos y

Q: nasin(hx) cos(bx)dx

A:

Q: SOLVE THE EQUATIONS

A: Given:

Q: 1. Integrate: e3x cos(x) dx

A:

Q: 1-[t2 cos at

A:

Q: Find integral.

A: We have to find the integral I=∫cos(5x) dx

Q: Example 1 Find dy/dx, if sin (²+3x+¹) b. y = cos²(2x-1)

A:

Q: 7. Compute •+∞ COS X x¹ + x² + 1 -dx.

A:

Q: Use linear approximation or differentials to approximate cos (1.6)

A:

Q: (In x |cos(In x) dx X.

A: Find integration

Q: 5. If the functions y = sin x and y = cos x are both subjected to a horizontal compression by , and…

A: y=sinx is subjected to compression by 13 y1=sin3x Then taking reflection in x-axis y2=-sin3x

Q: establish each identity.

A: Given  The identity is ln sec θ=-ln cos θ

Q: Find the general solution of y'= sin²xcosy.

A:

Q: 25. Find x, y, eR from 2coshy - 7sinhx = 3 and coshy - 3 sinh² = 2 %3D

A: The given system of equation: 2cosh(y)-7sinh(x)=3                    ......  (1)cosh(y)-3sinh(x)=2…

Q: 8. lim,0 1-cos x 2x2 1 (a) 1 (b) – (c) 0 (d) ; (e) 1. -

A:

Q: y = x cos(In x)+x² In x²

A: d dx(cosx) = -sinxddx(lnx) = 1xddxx2 = 2x   Product rule u.v = u'.v + v'.u

Q: Differentiate y=excos(x2): y'= A. excos(x2)-2xsin(x2) B. -2xexsin(x2) C. ex(cos(x2)-2xsin(x2))…

A:

Q: arctan(*) 1+e2kx dx =? A) arctan(e*)In|cos(arctan(e*)| + S in |cos(arctan(e**)dz]+ c kekx 1+e2kx B)…

A: ∫arctan(ekx)1+e2kxdxFormula to be used :1.Intergration  by parts2.Substitution3.ddxarctan(ekx) =…

Q: 2. Differentiate y os=1(-2x³ – 3)³ = cOs

A: From the given problem:   y=cos-1-2x3-33   As we know that:   cos-1x=-11-x2   So,…

Q: If f(x) = sin(x)e2x, then f"(x) = A) 3sin(x) e2x + 4cos(x) e²*. B) 3sin(x) e2x + 2cos(x) e²x. C)…

A: The given function is: f(x)=sin(x)e2x to find the second derivative f''(x). For that one has to find…

Q: 2 If the functions y = sin x and y = cosx are both subjected to a horizontal compression by what 3'…

A: Given: The function y=sin x and y=cos x are both subjected to a horizontal compression by 23

Q: In(x) limx→0* 0 e = 0 cos(re-x)+2

A:

Q: Find y' (y prime) and y" (double prime)y = cos(x2)

A: To determine the expressions for the first and second derivatives of the given composite function

Q: (e²)(sin²2x) Compute In y and In 5z

A: Basic log formula are applied to solve the question.

Q: 11. Sketch the phase portrait and bifurcation diagram near A = 3. %3D

A:

Q: For | cos 3x cos 4x dx :

A:

Q: A) /16 /2 cos (167 x5 ) dx dy. Os xs 2 Og ys x*

A:

Q: /16 cos (16л x5) dx dy. Os xs 2 Os ys x*

A:

Q: 2. y= 4sin(2x- T) and y= cos(3x-) 2

A: According to question given that y=4sin2x-πy=cos3x-π2

Q: Find (1,0) where y2 + x2 + eV = 0

A: Given y2+x2+ey=0 ⇒y2+ey=-x2⇒ddx(y2+ey)=-ddx(x2)⇒2ydydx+eydydx=-2x⇒dydx(2y+ey)=-2x⇒dydx=-2x2y+ey

Q: 2x Cos 23 find diy %3D

A:

Q: Show that d 1 In cos(x) os(x) - csc(x) dx 1+ cos(x

A: We have to proof

Q: Find 2 if x? cos4 cos* T. 1) 2xcos x+4x2cos3xsinx 2) 2xcos x- 4x²cos³xsinx O3) 2xsinx sin xcosx 4)…

A: Hence option (2) is correct.

Q: 2T COs x dx

A:

Q: 4) Find when y2 – x² + cos(x + y) = 0

A:

Q: find y prime and y double primey=cos(x^2)

A: To apply chain rule and product rule to find the first and second derivatives of a composite…

Q: The graphs of y = sin x and y = COS x are both sinusoidal. Which transformation performed on the…

A: The graphs of y = sin x and y = cos x are both sinusoidal. Which transformation performed on the…

Q: Compute cos(4x) -∞ (x²+2x+2)' dx.

A:

Q: b) 4 (€) -et cos (dt+물) cos (2dt +물) COS 3

A:

Q: .2 Suppose that w = x² + y² – z2 And x = psin(4)cos(0), y = psin(4)sin(0), z = pcos(4) Use…

A: The Solution is given in next steps

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.