1) 2² Evaluate ze x² + y² + 2 dv where E is the portion of the ball x² + y² + z² = 1 that is in the first octant.

Q: dx 19) u = 4x + 9 4x +9 1 A) B) 2/4x + 9 + C + C + 9)3/2 1 + C V4x + 9 C) 2- S dx 20) u == 4x + 6 4x…

A:

Q: 24. Given z = 6x°y-e", calculate or z. A) 12y–x'e" B) 12y-ye" C) 12y-e" ху D) 12x - хуе"

A:

Q: dx Evaluate: 1) 2) -2x 3) 4) 5) 5-y'

A: *** As per our guidelines, we are supposed to solve only the first three problems/subdivisions.…

Q: 4. (a) Prove, without recourse to geometry, that u • (v × w) = v • (w × u) = w • (u × v) = −u • (w ×…

A: Solution: To  solve  the  above  problem,  we  need  a  basic  result .Let  us  recall  that  first…

Q: Explain the process of parametrisation and also write 3 application ?

A:

Q: 7. Let B be the unit ball. Evaluate dxdydz √2+x²+y²+z²* Show the work!

A: We have to find the value of ∫∫∫Bdxdydz2+x2+y2+z2, where B is an unit ball.

Q: 18. а, 3 3+ (-1)"

A: This question is related to series and sequence.

Q: Consider the following bivariate data. Point ABCD EFG HIJ 0. 1 34 y 5. 8. 4 3 4. 1 1 (a) Construct a…

A: Hello, since your question has multiple sub-parts, we will solve the first three sub-parts for you.…

Q: dt 1). S V16-9t2

A:

Q: Prove that if Y:nz+P(x- mz) So thdz

A:

Q: 6. Evaluate: cin 4 a) (4x – 3) dx c) S* 2e* dx b) L, x²(-2x³ – 3)* dx d) ƒ dx e) S,(x + 1)(x² + 2x +…

A: (6) (a)To evaluate ∫254x-3dx Solution:…

Q: ) Differentiate: Y(u) = (u-2+u-³)(u³ + 3u?) и и

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…

Q: If F(x²_ye, ye-z?) = o then Prove that + XZ Z 2Z · Rx =

A: Given Fx2−y2,y2−z2=0 We have to show that yz∂z∂x+xz∂z∂y=xy The function Fx2−y2,y2−z2=0 can be…

Q: 69) 21) The tangent line of y = In(x² - 8x + 9) is horizontal at x = A) – 2 B) 2 C) 4 D) – 4

A: Given that: y=ln(x2-8x+9)

Q: Show that 6.8) fdx + gdy = Jc.8) (12,16) • (12,16) - (28x³3 By³dx + 35ytx dy) is independent of…

A:

Q: 8) Use the Trapezoidal Rule to evaluate V1+ x² dx;n = 3.

A:

Q: 4. a) Prove that i) V=1 ¡¡) fx+nh = Σk=0 I A I+A 1+A (1) Ak fx.

A:

Q: C = 3. 3. Find AB and BA given 3 A = and B = -7 -4 -2

A:

Q: 7)Debermine whether the inkegra) is covergant. Pivergank If its convergant, evaluate it.

A:

Q: 11. Find if y = va a) c) 2va 1/2

A:

Q: B. Non- homogeneous Higher Ordered LDE 2 1.D +50² + 8D -9) y - 69x²e-*

A:

Q: 12. What is the amplitude of the graph below? y 4 0 8+ 7+ 6+ 5+ 4+ 3++ -1- -3+ -4+ -5- -6+ -7+ -8+…

A:

Q: Find the most general antiderivative. | (7x3 - 3x + 2) dx A) 7x4 - 3x2 + 2x + C B) 21x2 - 3 +C C)…

A:

Q: 1) Find RT Y x+ 19 x + 15 R の

A: Here we have Y is mid point of ST and X is nid point of SR. Then we know that by the property of…

Q: Let G = (a, b | a² = b4 = e, ab = b³a). a. Express a'b’abab³ in the form b'a', where 0 < is1 and…

A:

Q: If hx) = Jx-4 then h*(-1) – h(20) is %3D a) 9 b) 5 c) 1 d) 4

A:

Q: 6) Find solution of the particular y"-2y'+y=x²-6x+ 2x

A: 6)Here the given differential equation is y''-2y'+y=x2-6x+2xe2exlet y=emx be the trial…

Q: 1 3 For V Vy evaluate y' when y = 4. A) 4 B) -4 C) -2 D) 2

A:

Q: 6) Show that (2xy, 2yz + x², y²) is conservative.

A:

Q: dx and u = 3x-2 1. y 2+1 + 3

A: