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Q: Use the given acceleration function to find the velocity vector v(t), and position vectors r(t).…

A: Accerelation vector  a(t)= 6i +9k  v(0)=3j and r(0)=0  Find  Velocity, position vector .

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Q: What is f'(x) given the integral function •5x+1 f(x) = 5x+¹ cos(e") du? ○ f'(x) = 5 cos (es) o f'(x)…

A: We have to find out derivative

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Q: Let r(t) = (e²t, e−³,5t) Calculate the velocity vector and the acceleration vector at t = 0.

A: r(t) = ( e2t , e-3t , 5t ) given  find velocity vector and acceleration vector    velocity vector…

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Q: H.W: Evaluate the integral 1. 30 [ (x²y - 2xy)dydx 0-2

A: Given: ∫03∫-20x2y-2xydydx

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Q: 03/ A. For the following function f(x). Find: ji. iii. m=? 1-4X m -UX.=-u P(1,-1) f(x)=x-2x² The…

A: See this solution in below

Q: 2. Find the equation of the line tangent to the circle x + y + 6x - 2y - 15 = 0 at the point (1,-2).

A: x2 + y2 + 6x -2y -15 = 0  given we have to find equation of tangent line to circle  for that first…

Q: 2. Find the equation of the line tangent to the circle x² + y² + 6x - 2y - 15 = 0 at the point…

A: Here the given circle is , x2+y2+6x-2y-15=0 We need to find the tangent to this circle at the point…

Q: 4. 4 1 [x²ydxdy 20

A: The objective of the question is evaluate the double definite integral.

Q: 11, 0-20² 2. 3. चं 5. T S cos 2x dx sin(²³) cos²(:-) / dx 2x-1 4x dx dx 6. 7. 8. S [² (x² + 0²³) dx…

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Q: a. For the following function, find f'(a). b. Determine an equation of the line tangent to the graph…

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Q: Find the limit. lim (x,y) → (5, 1) ety Discuss the continuity of the function. O continuous…

A: See this solution in below

Q: a. Use the definition mtan lim - h h→0 b. Determine an equation of the tangent line at P. f(x) = √5x…

A: topic- equation of tangent line to curve

Q: A submarine begins to descend at 9 meters per minute. It begins 15 feet underwater. A. Write a…

A: 1 metre= 3.281feet

Q: a Use possible symmetry of the graph to determine whether it is the graph of an even function, an…

A: Note : As per our company guidelines we are supposed to answer only one question. Kindly post other…

Q: Find d7 dx> d7 dx7 -(46 In(x)). -(x6 In(x)) =

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Q: Find the derivative of F(y). Select the correct answer. F( y) = sinh y tanh y F' (y) = sinh y sech y…

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Q: 11, 0-20² 2. 3. चं 5. T S cos 2x dx sin(²³) cos²(:-) / dx 2x-1 4x dx dx 6. 7. 8. S [² (x² + 0²³) dx…

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Q: Find the indicated limit by using the limits 6f(x, y) lim (x,y) → (a, b) g(x, y) lim (x,y) → (a, b)…

A: Given: lim(x,y)→(a,b)f(x,y)=3lim(x,y)→(a,b)g(x,y)=-5To find:lim(x,y)→(a,b)6f(x,y)g(x,y)

Q: 3) Consider the autonomous DE: y' = y² + 3y - 10 A) Find the critical points of the given DE.

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Q: Find a result by using exact for (sinxcosy)dx = -(cosxsiny)dy = 0 b. (x-6xy + y² + 10)dy = -(x² -…

A: I am attaching image so that you understand each and every step.

Q: Evaluate the integral. Select the correct answer. 1 15 cos ²6 x - = cos 6x + C cos³6 6x- 18 O…

A: Given :∫sin36xdx

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Q: 4. A one-way road has an overpass in the form of a semi-ellipse, 15 feet high at the center, 40 feet…

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Q: On which of the following intervals is f(x)=x4-100x²+x-10 concave up? Selected Answers: A. (-∞,-5)…

A: Concavity

Q: For f(x) = 7x and g(x)=x+4, find the following functions. a. (fog)(x); b. (gof)(x); c. (fog)(2); d.…

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Q: Solve the initial value problem y" + 10y' + 25y = 0, y(-1) = 5, y'(-1) = 3. y(t) =

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Q: Consider lim (x,y) → (0, 0) xy 20 X (see figure). 20 20 (a) Determine (if possible) the limit along…

A: Here to determine, lim(x,y)→(0,0)x2+y2xy

Q: Use Theorem on the derivative of the inverse function to find g'(a), where g= f-1. Calculate g(x)…

A: Here we have to find the inverse function and then its domain and range.

Q: Rewrite the expression In 3 + 5 ln x + 6 ln(x² + 4) as a single logarithm In A. Then the function A…

A: We know the property of logarithm that  ln(a)+ln(b)= ln(ab)  ...(1)  And,  pln(x)= lnxp .....(2)…

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Q: A department of roads and highways is doing a drive, a driver's rest area on the side of a highway.…

A: Ans=200 m  For detail...go through the solution...I have done solution in detail

Q: Note: Attempt All Questions Q1/ Answer the following: √4x5 2 16 45 A. Find the shortest distance…

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Q: Set-up and evaluate the triple integral for the mass of the box 1≤x≤2, 1≤y≤16, 0≤z≤ with √√y density…

A: To setup and evaluate the triple integral for mass of the box.

Q: Find the curvature K of the curve, where s is the arc length parameter. r(s) = (1 + s)i + j K = (No…

A: The given problem is solved below in detail.

Q: x ³³+ 2x² + 3x + 7 dx x²-x-6 S x³ + 2x²

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Q: 4. What is the length of the latus rectum of the ellipse whose equation is (x-3)² + 2 = 1. 25 16

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Q: Question 20 (5 points) Find the limit. 00 ∞ 5 0 -15 Question 21 (5 points) Find the limit. 0 1 00…

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Q: The base of a solid is the circle x² + y² = 9. Cross sections of the solid perpendicular to the…

A: Given: x2+y2=9

Q: √ grams/cm² and occupies Find the mass and the center of mass of the lamina with density 8(x, y)=-…

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