O fi[0,00)→R all continious Aunction aro Sx³f(x') dx = Sx f(x) abx %3D show this.

Q: Find the value df (a) that Make ECX) is Contincity at X- Ž

A: Given that :f(x)=cosx2x-π      ,             x≠012a2-3a+4      ,   x=0

Q: Give xy+x^2 y=2 such that dx/dt=2 in/sec. FInd dy/dt for x=1

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Q: Evaluate the line integral / (9x + 10y)dx + (5x – 6y)dy along the curve C : a = 6 cos t, y = 12 sint…

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = 7x2 – 3 dy =

A:

Q: Inx dx, 2. Integrate (1) using the substitution u = In x (ii) using integration by parts.

A: Integration by substitutions and by parts

Q: Let y=x2+2x. Compute Δy and dy at x=3 if dx=0.2. What is the difference between Δy and dy? That is,…

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Q: dx =- 1. dt dy at x = 2 if y = 4x° – 2 and dt %3D Find - dy dt

A: Given: y=4x2-2 and dxdt=-1 To find: dydt, when x=2.

Q: Evaluate the double integral : (y³ – 12x) dx dy -

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Q: Find dx/dt given that 4x^2+9y^2=13x  x=1,  y=-1 and dy/dt = 10

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Q: dy Find at x = dt dy dt || 4 if y = 3x² + 5 and dx dt = 1.

A: Let's find dy/dt value at x=4.

Q: dy 2х + ху is separable. dx y2 + 1

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Q: y, thên thế total differential of and y O df = 11 dr + 16 dy O df = 15 dr + 19 dy O df = 12 dr +18…

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Q: Compute the differential dy for y = (2x + sin x)². dy =

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Q: Compute /. x² dx dy dz, where E = {(x, y, z) : x² + y² < 1,0 < z < 1}.

A: To evaluate ∬∫Ex2dxdydz, Where E is the region E=x,y,z:x2+y2≤1, 0≤z≤1.

Q: dy Find for three only: dx 1) y = In(cos x . Inx²)

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Q: What is the integrating factor of the D.E. 2y dx + (x- sin vy) dy =0 ?

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Q: 3(1 + 2) - dy 2ty(y – 1) dt

A: The method to find the solution of the differential equation helps to find the required solution.…

Q: 2x,x X, +X, Find the total differential dy, given

A: Introduction: On an open set S, let z=f(x,y) be continuous. Changes in x and y are represented by dx…

Q: Evaluate the line integral / (7x + 5y)dx + (3x – 9y)dy along the - curve C: x =2 cos t, y = 4 sin t…

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Q: Evaluate sczxay) dx^ (x+ 3y) dy along the poth C: ure on y =1-3 from l0,)) to Cl,0)

A: Line integral problem......

Q: -dx. V1–16z² Consider For the u-substitution u = 1 – 16x², which is the new integrand in terms of u?

A: Given:-∫014x1-16x2dxTo find: new integration in terms of u by using the u-sbstitution, u=1-16x2

Q: A particle moves on the graph of y^2 = x + 1 so that dx/dt = 4x +4. What is dy/dt when x =8 ?

A: We have, a particle moves on the graph of a function given as y2=x+1 Differentiating both of the…

Q: d²y 1.) of y = sinInß and x = In(Inß) dx2

A: Topic = Derivative As per guidelines , At a time only one question can be answered out of different…

Q: Find the differential dy. x + 3 4x - 1 dy =

A: y=x+34x-1

Q: given xy+x2y=2 such that dx/dt=2 in/sec. Find dy/dt for x=1

A: Consider the equation and

Q: find dy&gt;dt.…

A: Given function, y=ecos2pt−1

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = 7x2 − 3 dy =

A: Given y=7x2-3 Differentiating both sides: dy=14xdx

Q: Find the differential dy of the glven function. (Use "dx" for dx.) 7 y = 3Vx + dy =

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Q: Solve the D.E [y(++csy)]dx + [x+Inx-xSiny] dy-o

A: Solve de

Q: Find the differential dy. y = ex/2   dy=

A: Here the given expression is y = ex/2. Apply the chain rule:

Q: Find the Wronskian for the differential equatio: dy dx2 fip dx 3 10y = 0

A:

Q: dy Find at x = dt dx - 1 if y = 2x? – 3 and dt - 2. dy dt ||

A: y = 2x2 - 3dxdt = -2dydt = ?   at x=-1

Q: solve: d/dx on the intergral 2x to x3 with an integrand of t2 et^5 dt

A: Given integral is

Q: Find the general and particular soulution of dy/dx=3y, where y=6 and x=0

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Q: Find dy at x = -1 if y = u’ +5u – 4 and u = x² +x . dx

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Q: The Integrating Factor for the DE y dx = (ye' – 2x)dy %3D is: -2y レマ None of These 2y

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Q: Evaluate the line integral (6x + 8y)dx + (3x – 3y)dy along the curve C: x = 4 cos t, y = 8 sint…

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Q: From an integral equation corresponding to the diffrential equation d'y +x + y = 0 with the initial…

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Q: ve the given differential equati dy dx - (1 + x)y = xy

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Q: Siny dx t sin Zydy + x dy

A: To solve: sin⁡ydx+sin2⁡ydy+xdy=0…

Q: dy at x=0. dx If y = (3x² + 4x + 5)(e* – cos 2x), then find %3D -

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Q: Use the differential dy to approximate Ay whenx changes from x = -2 to x = -1.96. %3D y = x² + 1

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Q: Verify the linear approximation at ( 0, 0) for e^x cos(xy)

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Q: Explain, the given differential 3x²dx + 2yz dy + y² dz is exact or not.

A: We will check whether  3x^2dx+2yzdy+y^2dz is exact or not.

Q: Q3) Evaluate triple integral dz dx dy.

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

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Q: dx o ex+x е. f. S sin(vE) dt S dx 2x cos(vE) dt COS g. dx 'x

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Q: What is the integrating factor of the nonexact DE (4xy + 3y – x) de + æ (x + 2y) dy = 0?

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Q: dy dx 2 at x = 5 if y = 4x? + 5 and dt = 4. Find %3D dt

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.