= (1 – t)i + (4 + t)j ess your answer as an ir erical answer only.

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A:

Q: xpáp -1 dydx In(y)

A: Since you have posted multiple questions I can do first question as per our company guidelines…

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A:

Q: dy Find for the following by using appropriate rules: iv. x² + y3 + (lnx)e♥ = 4. y = Vx(3x2 – 1) V.

A:

Q: The DE : y' = e>x-7V is seperable Select one: O True O False

A: Try to separate the variables if it is possible than given DE is separable.

Q: 10e? dz by residue theorem, where C'is the contour z| = 2 1:4 + 52ª Evaluate

A: Complex integration

Q: EX. Evaluate the JoJex*+2xy+y*) dydx when step size of X = 0-2 and step size of y=o.5?

A:

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A: To find x, and y for the below complex number. −i+12−i

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A: Solve the differential equation

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A:

Q: I shift as in Example 4.9 to find the general solu b. (2D – 1)²y = 0 + czx?)e2x

A:

Q: D Express the interval in (a-k, a+R) aad 1 x.-alc.R I(3x+1)?(<!

A: |(3x+1)2| &lt;1 both side we take square roots |3x+1|&lt; +1 3x+1 &lt;+1 3x+1&lt;1    or    3x+1&lt;…

Q: Hawis Find d Vand V2if vI+2V2=31-k and 3V-V2 si+j+k

A:

Q: x=In i y=r2, find y " when For x=0• O 8 O 4 O 16 O 2

A:

Q: F ind the Gth roots af 4 +jA Vs.

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: dz where C is the bo + 6)

A:

Q: R. 4. Use the information in the figure and prove that VC = CX, making use of reflec- tions. [UCSMP,…

A:

Q: dz where C is ned by x = 0, :

A:

Q: T scosce) 25-r2' 2. dz dr de 0 0

A:

Q: 8. Let D be the rectangle given by -1<ys0, 1s x< 3. calculate ff,(x2 + y)dydx

A: 8. We will evaluate the given double integral. Given integral is ∬D(x2+y)dy dx with the limits…

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A:

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A: The given differential equation is y't=ky+b and the function is yt=Cekt-bk

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A:

Q: Show that S> 0.

A:

Q: -dz < 2re?. z + 1 Jェ-1|=1

A:

Q: The reverse order of J Só 3xe dydx is equal to 2(e - 1) е - 2 -e

A: After changing the order of integration, solve it.

Q: r In y dr, where D is described by 1 < r < 2, e <y<e aD | V1 +r² dy, where D is described by -1<r<1,…

A:

Q: Find r'(t) = 8Vti + t?Vij + In(z²)k r'(t) =

A:

Q: There does not exist r E Q ə r² = 2 ylgn ihi

A:

Q: Prove that : V.(V×A)=0

A:

Q: x(t) = 121? – 12t, y(t) = -41 + 612 + 9t %3D %3D where t goes from 0 to 1. Answer:

A: Solve the following

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A: To find particular solution of D.E.

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A: Given, s = -3tant -e-t   We have to find the value of dsdt

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A: We will solve the following.

Q: S- - ydx + xdy, C: y² = 3x from (3,3) to (0,0) 01 0 3 O 0 2

A:

Q: (xiv) f(t) = 3+et – te-2t + e5t cos3t + 6sinh7t

A: As two questions are given , I will solve only the first one. Given : f(t)=3+e4t-te-2t+e5tcos3t+6…

Q: Ext-Let X ond Y ave tno V-r1w.th jf.alf (291+9) 42

A:

Q: dy Given a DE of dr 1-z-y using simple substitution, what must be your z? z+y Answer: ||

A:

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A:

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Q: z) = x' - 4r – 12:r² + 32z + 1- by commas. Enter exact values, not de

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A:

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A:

Q: Y = / x² g 4-Jx²_s %3D 2

A: Given function : f(x)=x2−94−x2−9

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A: we have to find derivative

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A:

Q: Find the general şolution to the following (D* - 2D – 7D² +8D+12)y = 0|

A:

Q: (a) Find where x² + 3xy + y² = 3 at (√3,0). da

A: topic- implicit differentiation