Find r(t) if r'(t) = 4t³ i + 5t+j + √tk and r(1) = i + j. r(t)

Q: . Calculate the area of the region lies inside the diagram (r = 4 cos 20) and outsid the circle (r =…

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Q: 3. Choose three vectors: and Use these vectors to verify the associative property.

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Q: MTI THE - T C₂ b

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Q: X3-4X Which of the following graphs represents the function 1(x)=2x²+2x-4 -? 5 1 2 f(x) O O 4 7

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Q: Find the solution of the given initial value problem in explicit form. 1 y′ = (1 — 13x)y², y(0) = 6…

A: We can solve the given initial differential equation .

Q: 4. How many solutions are there between the plane P₁: (x, y, z) = (4, −3,−1) + s(1, -3,1) + t(2,4,…

A: Plane and line

Q: Prove that: 1- Cos (2) dxdy (¹) where R the region bounded by x+y=1,x=0.y=0

A: Given integral I=∫∫Rcosx-yx+ydxdy Where R is bounded by x+y=1x=0y=0

Q: You are driving a car away from home. Your velocity (miles per hour) t hours after noon is given by…

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Q: Find an antiderivative for each function when C = 0. a. 1 b. 2√x 1 c. ²{√x + 7/7 C. a. The…

A: Formula ∫ xn dx=(x(n+1))/(n+1) +c

Q: State the order of the given ordinary differential equation. (1-x)y" - 5xy' + 2y = cos x Determine…

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Q: Find the general solution of the given differential equation. x²y' + xy = 8 y(x) = Give the largest…

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Q: ل 2 ل وه هه ** ** " سم Z || . 1

A: Given problem:-

Q: 8-9 Let A = 2 3 (a) Find 5A +6B. 5A +6B = and B= 9-2 Complete parts a through d.

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Q: Lesson Performance Task At an amusement park, a person spends $30 on admission and food, and then…

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Q: Solve the differential equation (18xy + 18y²)+(6x² + 18xy)y' = 0 using the integrating factor u(x,…

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Q: Find an explicit solution of the given initial-value problem. 없을 y(7) = 7 1

A: Find an explicit solution of the given initial-value problem.         dydx=y2-1x2-1  ,    y7=7

Q: ¹.) f(x) = (x³ - 7x² - 6x + (4 +17) f(x) = x-6 7x - 6 2) f(x) 4 - 17x²

A: Explanation of the answer is as follows

Q: السؤال الثالث Question Three * Q3. For the motion vector r(t) = et cost i + et sint j , find: (i) N…

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Q: Find the general solution of the given differential equation. xdy+3y=x²-x dx y(x) = Give the largest…

A: The objective is to solve the above question.

Q: Find the solution of the given initial value problem in explicit 1 y' = (1 — 11x)y², y(0) = ——— 6…

A: We can solve the given differential equation by using the variable separable method.

Q: First verify that the given vectors are solutions of the given system. Then use the Wronskian to…

A: Concept: Wronskian method: W(x1(t), x2(t), . . . , xn(t)) =x1(t) x2(t) · · · xn(t) xx1'(t) x2'(t) ·…

Q: 1. f(x¹ + x³)dx π

A: The objective is to find the integration.

Q: Determine whether the Mean Value Theorem can be applied to f on the closed interval [a, b]. If the…

A: The objective is to solve the above question.

Q: Find the solution of the given initial value problem in explicit form. 1 y' = (1 – 3x)y², y(0) = 8…

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Q: Let f(x) = 2x² - 4x and g(x) = -3x - 1. Find f[g(-4)]. f[g(-4)] =

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Q: Determine whether the series is convergent or divergent. If it is convergent, find its sum. 9 27…

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Q: Q5) Solve dx dx +2xy = 3 by using Euler's method to find the approximate solution up to X-2.9 when h…

A: The solution is given below

Q: Q.2)(A) Find a formula for the area of the triangle in the xy-plane with vertices at A(0, 0), B(a₁,…

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Q: Find the derivative of each of the following functions using any method. 4.) f(x) =…

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Q: Q5) Find dw/dt at the given value foe the following functions 2) w = 2ve* - lnz.x = ln(t+1), v =…

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Q: Find the general solution of the given differential equation. xdy-y=x² sin x yw Give the largest…

A: Explanation of the answer is as follows

Q: Determine whether the differential equation (4x² − 2xy + 6) dx + (2y² − x² + 4) dy = 0 is exact. If…

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Q: In this problem, y = c₁e*x+c₂ex is a two-parameter family of solutions of the second-order DE y" - y…

A: The given differential equation is;  y''-y=0, y(-1)=6, y'(-1)=-6.

Q: Find all relative extrema of the function. Use the Second Derivative Test where applicable. y = x²…

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Q: Use the graph to determine the limit. (If an answer does not exist, enter DNE.) y (4, 3) C = 4 X 4…

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Q: The normal line to a curve h(x) = -x² + 1 at point Z, is defined as a line that passes through point…

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Q: dx 10) √x²4(14+x²) a) - - - c) - 1 4X ㅗ 4x + 1 andan ²/3 + c autan 1/2/3 + c 8 I ondan 2/2 + c 8 j 8

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Q: Solve the given differential equation. All solutions should be found. dy 3x² - 4y - y³ 4x + 3xy² dx…

A: Explanation of the answer is as follows.

Q: dy Find by implicit differentiation. Then find the slope of the graph at the given point. dx 3x³y =…

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Q: ९२ e 17 olx

A: ∫1e2(1-x)/dx2x here integration is given  ∫1e2 dx/2x - ∫1e2 dx/2 (1/2)[lnx]1e2 - [x/2]1e2 (2-ln1)/2…

Q: 7) Find the area of the region enclosed by the cardioid r² = 4 cos 20.

A: To find the area of the region enclosed by the cardioid r2=4 cos 2θ.

Q: Find the arc length of the curve y = 2/3 (x − 1) raise to 3/2 on the interval [2,3]

A: We have to find the arc length of the given interval [2,3] .

Q: B) Evaluate the line integral of the function P(x,y) dx + Q(x,y) dy. over the curve C where…

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Q: :a stream function is given by: Y=2x²y + (x+t)y2 Find the velocity equation for flu me = 1s?

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Q: Verify the product law for differentiation, (AB)' = A'B + AB' where A(t) = To calculate (AB)', first…

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Q: area enclo fencing is m². Fence ε = www. 10x Building

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Q: Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had…

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Q: State the order of the given ordinary differential equation. (1-x)y" - 8xy' + 3y = COS X

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Q: Use Lagrange multipliers z = f(x, y) = x² − xy + y² to find the absolute maximum and minimum values…

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Q: x -2x +x= 15; x (0) = 7, x (0) = -16

A: This question is based on diffrential equation solved using Laplace transform.