Q4) Consider the following D.E. (x³y + x³+y+1) dx + x² e dy = 0. Then one of the following is true: (A) The D.E. is separable. (C) The D.E. is exact. (E) The D.E. is Bernoulli. (B) The D.E. is a first order linear D.E. (D) = x is an integrating factor.

Q: HW_2: If Z - N(0,1), find a) p(Z > 1.2) b) p(-2 < Z < 2) c) p(-2 < Z < 1)

A: Solution

Q: Find the value of c such that S xe = 3.

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Q: 1.n f csc n? de y2 - 2y + 3 2.5; Vy - 3y: + 9y – 21 dy

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Q: 7. Find Lt V1+P

A: Introduction :

Q: Tgir.y) = (2ry, 1+2+) and g(1.0)=8, then g(4.1)-9(2.1) =

A: Topic:- calculus

Q: EVALUATE Sx csc(2x) cot(2x) dx A. -z csc (2r) +in esc (2r) - cot (2-)| + C В. B. z csc (2z) + In…

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Q: If z =t cost, y =tsint, z=t, then x² + y² = t² cos²t+t² sin² t = t² = z², so the curve lies on the…

A: Given x=tcost, y=tsint and z=t and z2=x2+y2 Substitute x=tcost, y=tsint and z=t in z2=x2+y2…

Q: and B =

A: (2/5,1/5,1/2)

Q: (In æ)" Find y'. Let y = e" + 2

A: Explanation of the solution is given below...

Q: If V = Ai - j +sk and Vz= 41+2j +4k, Find Value of (A) so that the length of Projection of V ont Vz…

A: Use the formula for length of projection of a vector onto another vector

Q: XI. 6 F dF where F = (x³ – y, x + e') and C is triangle with vertices (0,0), (3,0), (4,2).

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Q: e equation of

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Q: Q.3) Find the constants a, b, c, d, e if f(z) = (ax³ + bxy² + 3x² + cy² + x) + i(dx²y - 2y³ +exy +…

A: Given :  f(z) = ax3+bxy2+3x2+cy2+x + idx2y-2y3+exy+y  is analytic. To find : The constants a, b, c,…

Q: a b. d and assume that det(A) = 10. Find det(3A), det(2A-1), det(2A²), det(3(A")-1). (a) Let A = f…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Evaluate the following 1, $(3x – y)dx + (x + 5y)dy ,where C = x² + y? = 1 2.6(2y + 1+x5)dx + (5x –…

A: We have to evaluate the line  integral over the closed curve . Here I am solving first question if…

Q: 2. Which of the following is the domain of y sec(x)? %3D A. [-1,1] B. R- (n+ 1) C. IR D. [-1,0}

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Q: Compute e-1/z ₁-3+1° -dz, and $ e¹/2² |z-i|=3/2 2² +1 dz.

A: Concept Used If a complex function f(z) is analytic within and on a closed contour c inside a…

Q: b) By using the given substitutions, show that i. Sx(x – 3)5dx =÷(x- 3)“(2x + 1) + C, z = x - 3 14…

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Q: 3. V4- (x – 3)²dx.

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Q: ut. (b) 710 - 76 72 (c) m*n (e) m m2 ÷ m* (f) -25A

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Q: The circle æ² + (y– 1)² = 4 has center (0, 1) and radius 2, so by Example 4 it can be represented by…

A: The parametric equation of the circle having center at a,b and radius r is: x=a+r costy=b+r sint…

Q: 国~ Let aj = a2 -24 and b: For what value(s) of h is b a linear combination of aj and a2?

A: Explained below

Q: Zad. 1. Check if the function y is the solution to the given equation: b) e¹=1-e, e¯' (1+y')=1 in…

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Q: w = (1³ + 11)8| dw dt

A: Given :   To find

Q: Evaluate the following 1, (3x - y)dx + (x+5y)dy where C = x +y = 1

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Q: Let A + 0 and ACB. Show that NB CNA.

A: Given :A≠∅A ⊆ B