y= e fonksiyonunun d'y dy 11 + 27y = 27e dr 11z dr?

Q: xp %3D 0. dy %3D 18 + 9t2 dt xp for y = Find ||

A:

Q: dy If y = (t + 6t + 4) (3t2 + 4), find dt dy %3D dt

A: it is required to find the derivative.

Q: Find dy/dæ in terms of t if x =t – t°, y = 2+ 4t dy/dx =

A: The differentiation of parametric form of functions can be done by using the formula,

Q: dy In(3x + 7) Find for y = dæ 9e5z dy %3D dx

A:

Q: dy Find - for y = du dy du = = [19+ √9 +10t2 dt. 0

A: given y=∫0u9+10t2dtTo find: dydu

Q: . (4fy – 152 – y) dt + (tª + 3y² – t) dy = 0

A:

Q: Q1/ Evaluate So (x² + 3y²) dy dx using Simpson's 1/3 rule in x-axis and Simpson's 3/8 rule in y axis

A: 1 Given integral is ∫03∫01x2+3y2dydx. We have to evaluate the given integral  by using Simpson's 13…

Q: Q2. Show that dx ax + by di dy = cx + dy di can be written as + yx = 0

A: The given system of differential equation is. dxdt=ax+by                     ......1dydt=cx+dy…

Q: dy If x = t - t3 and y = t2 - t, the value of at t = 2 is %3D %3D dx

A:

Q: dy If y = (t + 2t + 8) (6t² + 6), find %3D dt dy dt

A: The given question can be solved as shown in step2.

Q: Evaluate: S. yx2²dx + xzydy + xz²dz, where C:x = sint, y = cost, z = t² , (0 <t< 1).

A:

Q: Find dy/dæ in terms of æ and y if æ°y – x – 2y – 1 = 0. dy dx

A: We have to find dydx in terms of x and y if x3y-x-2y-1=0.

Q: dy dt t2

A:

Q: dy Find for y = dr dy dr || r J√3 + 0 3 + 4t2 dt.

A:

Q: dy = 9 +y osx dx

A: Given

Q: If x = 2t2 +t+1 and y=8t3+3t? + 2 then dy at t = 1 is dx

A:

Q: dy Given that y = 5u+ 4 and x = -u', hence find dx

A:

Q: zl*dz, where C is x(t) t2, y(t) , t:2 1 Evaluate /=

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

Q: If f(x, y) = xy + 3xy2 then df find at (1,2). dy

A: The function fx,y=xy+3xy2 then we have to find ∂f∂y at 1,2.

Q: dy/dt= 2e-t/8, t is greater than or equal to 0

A:

Q: Find dy if x=t+6f and y= dx 2 5 at t=1 +

A: We have to find dy/dx

Q: ) y = 3logst ) y deriv = (sech t) (1 - In(sech t

A: A function's derivative is the function whose value at x is f′. (x). The graph of a function's…

Q: Exercise 1. find the differential dy (la) y = 3z? (1b) Find y = V9 - z2

A:

Q: Evaluate: S. yx²dx + xzydy + xz²dz, where C:x = sint, y = cost, z = t?, (0 <t< 1).

A:

Q: dy Find for y = /12+13t dt. dv

A:

Q: (e) dy if y = (t +1)(t + 9) %3D dt It%3D3

A: Given that y=(t2+1)(t+9)

Q: || (z, y) dy de = f(r,y) dx dy 0. Jo Jo O Tryc

A: Solution: The objective is to select the correct option

Q: If y =Aex +Be™ d'y -(m+n) dy. Show that + mny = 0 dx

A:

Q: dy if y = vt' -e' and x = dx Determine In(6t)

A: dy/dx = [7/2 t^5/2 - e^t] [ln(6t)]^2/ t^2 [3ln (6t) -1]

Q: If y = (t² + 2t + 6) (3t² + 5), dy find dt dy dt ||

A: Given function: y=t2+2t+63t2+5 We have to find dydt

Q: d²s ds + dt 4t + 2cost where s = 0, ds/dt = 0, t= 0 dt2

A:

Q: Given z=200st+17 and y=9sint dr dt dy dt dy da %3D

A: First of all we will differentiate the given equations with respect to t

Q: %3D y"(t) = 4y(t) – e-tU (t – 1), y(0) = y'(0) = 0.

A: Solution

Q: dy of y=X Find

A: y = x^x Find dy/dx

Q: 2 In(t) and y=4 t2 then find %3D %3D dy dx d'y dx2

A:

Q: y = secx prove that d² y dx +y 2y

A: For y=sec x, we need to prove that d2ydx2+y=2y3. Here,            y''=secx''      =secxtanx'…

Q: Evaluate: S. yx²dx + xzydy + xz²dz, where C:x = sint, y = cost, z =t², (0 <t< 1).

A: As per the question we are given a line integral, which we have to evaluate around the curve C.

Q: dy Given that y = find . dz'

A:

Q: dy/dt=0.3(y-200) y=70 when t=0

A: Given differential equation is

Q: dx Find the value ofat y=2 if x=z³+5z and z= dy (y² + 2y)'/³. -

A: Consider the function, x=z3+5z Differentiate 'x' with respect to 'z' as, dxdz=ddzz3+5z=ddzz3+5ddzz…

Q: Es cierto que I[ (* + v9) sin (a*y² ) dz dy < 9 0. Seleccione una: O Verdadero O Falso

A:

Q: dy If y = (t + 6t + 5) (6t² + 6), find dt dy dt ||

A:

Q: what is the equilibrium of dy/dx = y - sqrt(y) when y >0

A:

Q: ds where t+s = 2s . dt Find %3D 6.

A: t+s=2s

Q: dy Find dt y = 3t(21 – 5) $ II 히

A: The product rule of differentiation states that ddx[f(x)g(x)]=g(x)ddxf(x)+f(x)ddxg(x) The chain rule…

Q: dy dæ at x = 2 if y = 3x + 5 and dt Find - 2. %3D %3D - dt dy %3D dt

A:

Q: If z'y +y = r dy 1, then at (0,-1) is

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: dy/dt=0.3(y-200)

A: Separate the variables and integrate both sides.

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.