Q4 A) Calculate the divergence of the vector field F=y³i + xyj B) Find the Curl of F(xy.z)=3x²i + 2zj - xk.

Q: Evaluate: ²₁²²-²² du (x²-y²)²] S du dt x+y

A:

Q: Using the Mean Value Theorem, given f(x) = x³, what is/are the value of c, where 0 < c < 2 such that…

A: Topic = Functions

Q: Evaluate: xy² dx dy [√ 0

A: We have to find value of given definite double integration.

Q: Evaluate: ƒ³, ƒ²₁ √√₁²[z³(x + y)³] dz dy dx -3

A: Given :∫-33∫-12∫01z3x+y3dzdydx

Q: 1. Show the drawing and entire solutions to know the differential equations of the lines' families…

A: As per our guidelines we are supposed to answer only one question at a time. Kindly repost other…

Q: S77/2 Su² sin (=) dt du Evaluate the integral: f/2.

A:

Q: 4. Evaluate the double integral: Y SZ (Hint: Change the order of integration to dy dx.) dx dy. +1…

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Q: Evaluate: SS₂₁ (4x²y — z³) dz dy dx

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Q: What will be the orientation of the curve of the graph of the function f(x) = on (-3,0)? A.…

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Q: Evaluate the following * S sin(4x) dx O cos(4x)/4+C -4cos(4x) + C O-cos(4x)/4 + C O-4cos(4x) + C

A: We can find the answer as below.

Q: f(x)=2x+1(3x-1)

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Q: A piece of wire 20 m long is cut into two pieces. One piece is bent into a square and the other is…

A: Please refer to the image below

Q: Given f(x)=x²-1 on [-2,2]. a. Find the critical numbers of f on the given interval. b. Determine the…

A: A critical number of a function of a single real variable, f(x), is a value x0 in the domain of f…

Q: Ex. Find the general solution to dy 1 -2.x dx X -

A:

Q: Evaluate the integral: S/2 sin(4t - u) du dt

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Q: 1. Find the Inverse Laplace Transforms of the following. 4 1) -1 S-3

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Q: Q3/ Use the definition of derivative to find f'(x) where fx=- 3 X+1

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Q: A stone, projected vertically upward with initial velocity 112ft/sec, moves according to…

A: Topic = Algebra The maximum height reached by the stone is 196 ft.

Q: ¡xr-¹e-λx, x>0, r,λ > 0. Given f(x) Γ(r) 1. Find f(x)dx.

A:

Q: 2. Evaluate all of the integrals. a. [² sec²rtan r (1+sec x)² dz

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Q: 2. Evaluate the double integral that will find the volume of a solid bounded by 21-2y²-322 and the…

A: Given: z=1-2y^2-3x^2 and xy-plane

Q: 2 (xy + x) dx = (x²y² + x² + y² + 1) dy Oln(x² + 1) = y² – 2y — 4ln|c(y + 1)| O In (x² + 1) = y² +…

A: We have to solve given differential equation.

Q: Given f(x) = a-1 5xª−1(1 − x)b−¹,0 0. Evaluate ſ*x* f (x)dx. HINT: Express B (a,b) (¹ rk f(x) dx as…

A: Let's evaluate given  expression.

Q: hi what is the simplified final answer of this?

A: Given problem:-

Q: Give 1 problem of partial differentiation of function of U with respect to 3 independent variables…

A:

Q: t = b? Choose 1 answer: b Ⓒ / ° v A a © B Ⓒ a b cb a a b e20t+t6 dt e10t+t³ dt 10e10t+ 3t² dt…

A: Topic = Integration

Q: 4 Find the area of the region bounded by x = 2y²+1 and the y-axis using the horizontal strip.

A: Given: x=42y2+1

Q: If the total cost function is given by TC = 300+5g+then the marginal cost function MC = Ⓒa. 5g + / 3…

A: We have to solve the given 2 question.

Q: The value of A. +3+2x² +C C = 1 + x² +2+C 20 [ (² + 3) *²x² dx B.+²+3x³ +C D. none of the answers

A:

Q: The 7th derivative of f(x) = 3x5 - 12x¹ + 7x³ − 11x² + √5 with respect to a is O 360T O none of the…

A: Topic = Derivative

Q: A stone, projected vertically upward with initial velocity 112 ft/sec, moves according to 8 = 112t -…

A: We have to choose correct option

Q: 1. Find the cofactor of 6 in matrix D 9 8 4 2 -9 3 4 D= -3 2 3 3 2 968 7 6 (8 9

A:

Q: [x³ In 4x dx A) _ x4nux - A x +C oA nixt dx4+c 4x 16 B) In 4x xr…x4.C D) =xAndx- +x4+C

A:

Q: Evaluate: ₁³(x + y)³] dz dy dx S²³₁

A: A detailed solution is given below.

Q: 3(a) The cost of manufacturing motor cycles (per day) is related to number to number of motor cycles…

A: Here we have to use the concept of derivatives.

Q: What is y' of y = sin¹ (cos x)? O A. y' = ATHE sin + 1-cos² 1 O B. y' = 1 OC. y'= sin z 1-cos² z OD.…

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Q: Find the point on the line y = 7x closest to the point (1, 0). (Use symbolic notation and fractions…

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Q: 3. of the solid enclosed by the hyperboloid z = Set-up the iterated double integral in polar…

A: Given

Q: 1. Simplify. Write "undefined" for expressions that are undefined. 1 -6 030-0 [B]- 4 + 5 -2 4.)

A: To simplify.

Q: Evaluate: ₁₂₁(4x²y — z³) dz dy dx J1

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Q: A particle is moving along the curve whose position vector is given as R(t) = (t)i + ( În (cost)) j…

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Q: What is the slope of the tangent line to the curve y = T I 7 O-2 02 0 - 17/12 01/1/01 O none of the…

A:

Q: Find the area of the region bounded by the curves 1 y = (x+8)2 y = 4 and the x-axis using vertical…

A: Explanation of the answer is as follows

Q: Determine the intervals on which the function is concave up or down and find the points of…

A: topic- inflection points and concavity

Q: 312-3x| dx

A:

Q: Evaluate: ³4₁ [2³(x + y)³] dz dy dx

A: To evaluate the given integral.∫-43∫-12∫01z3x+y3 dz dy dx

Q: 5x 2 Evaluate: ²3x²dz dy dx 2

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A: Given that  The Region bounded by the curves  y = 4 + sec(x) , y = 6 ,  -π3≤x≤π3  about y = 4…

Q: mydx = nxdy

A: answer is in next step . please give a like !!!

Q: on The radius of the sphere is decreasing at a rate of 2in/min. What is the rate of change of its…

A: