Use x = au, y = bv to show that the area of the ellipse x2 y? = 1 is rab. 62 a2

Q: lim (In ( V13x² + 9 (x) uj - (6+ - In X00 (Express numbers in exact form. Use symbolic notation and…

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Q: Evaluate * | (0² + 1) cos 0 d0. e2sine + 20cose – sine + c 02sine – 20cos0 – sine + c Option 1…

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Q: Matching Type. Match Column A with Column B. Write the letter of your choice from Column B in the…

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Q: Perpendicular to each of the planes x – z+ y = 0 and 2x + z – 4y = 5 and containing the point (4,…

A: We have to find an equation of the plane which is perpendicular to each of the planes x-z+y=0 and…

Q: Find the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the…

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Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

A: Solution is given below

Q: Question Is S (;x² + 5x + C)dx = 3x + 5 correct? %3D CLAIM EVIDENCE REASONING

A: ∫  3x2/2 +5x +cdx now integrate it 3x3/6 + 5x2/2 +cx +c x3/2 + 5x2/2 +cx +c this is the answer  so…

Q: 2-4х3 3. lim х--0- 5x2+3x3

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Q: e following: (x) = 2 + x – x², [a,b] = [0,3], p = 1 %3D he two conditions of the IVT are satisfied.

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Q: 10 2. f(x) dæ y=f(x) А1 АЗ 3 5 A2 A4 7 10 (figure is NOT to scale) the area of region Al is 6 • the…

A: Given query is to find the value of the indicated integral.

Q: 3. y = Arccos ( logx);y' = * O -1/x In(10)*sqrt ( 1 - (logx)^2) O 1/ x In(10)*sqrt (1 - (logx)^2) O…

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Q: it. notation and fractions where needed.)

A: We have to find the value of the given limit according to the rule of limit

Q: Find the area of the triangle with vertices P(1, 2, –3), Q(0,0,0) and R(3,4, 1). NOTE: Enter the…

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Q: Find the vector component of v = 2i – j+ 3k along b = 6i + 6j + 7k and the vector component of v…

A: Given; v=2i-j+3k ; b=6i+6j+7k   We know that the expression; The vector component v along b=v·bb2b…

Q: Explain why S is not a basis for R2. S= {(3, 5), (1, 0), (0, 1)} O sis linearly dependent. O does…

A: The given set S=3,5, 1,0, 0,1

Q: Find the directional derivative of f(x, y) at P(5,0) in the %3D x + y direction of Q(3, –3). NOTE:…

A: f(x,y)=20x+y

Q: Determine whether the sets S, and S, span the same subspace of R. s = ((0, 0, 1). (0, 1, 1), (8, 1,…

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Q: x = -4 + t, y = 2t, z = 7 + t (a) (0, 8, 11) O Yes O No (b) (4, 5, 9) O Yes O No (c) (-6, -4, 5) O…

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Q: whetr he se linea bendent or linea dependent. S - {(-5, -3, 6), (2, -3, 1), (9, 0, 0)} O linearly…

A: To solve the following problem

Q: Find dx (9x² + 16 1 1 - In |3x + V16 + 9x²| + c -In |3x – V16 + 9x²| + c Option 2 Option 3 1 1 In…

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Q: (a) Oppositely directed to v = (3, -4) and half the length of v. %3D W3= (?, ?) (b) Length V5 and…

A: To Find : a) A vector which is oppositely directed to v=<3,-4> and half the length of vb) A…

Q: endicular to the plane z + 3y – x = 7 and containing the points (2, 5, 0) and (0, 2, -1)

A: Here we have to find the equation of plane which is perpendicular to the other plane.

Q: 6- 5- (3,4) (0,3). (3, 2) (-2, 1); (3,0) 3 12 :1 2 4 6 Find the limit lim f(x) lim f(x) а. b. lim…

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Q: (0³+ 38+ 3D+ 1)y-8sinx ylo): -/ y'l0)= 3 y"16)=5 5-

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Q: When a factory operates from 6 AM to 6 PM, its total fuel consumption varies according to the…

A: Solution )  f(t) = 0.8t3 - 0.3t0.4 + 27  Differentiate with respect to t  f'(t) = 0.8 × 3 t3-1  -…

Q: 1 Suppose that L is a location function of an object, given as L(t) = We will compute the 3t – 2…

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Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan L, , (3,…

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Q: Use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

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Q: Find the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the…

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Q: The term t (in years) of a $200,000 home mortgage at 7.5% interest can be approximated by the…

A: Given that the term t of a $200,000 home mortgage at 7.5% interest can be approximated by the…

Q: Find two unit vectors in 2-space that make an angle of 45° with 7i+ 6j. NOTE: Enter the exact…

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Q: U(r)= 1/r ln(aX^r+bY^r) U’(r)= ?

A: Here, U(r)=1rln(axr+byr)

Q: A snowball is thrown upward from a bridge into a river below. The function f(t): above the surface…

A: f(t)=-16t2+47t+88t=0f(0)=88gives the bridge's height.Brige's height =88 feetB)When the snowball hits…

Q: sin r da 4.

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

Q: dy = x and find the particular solution when y(0) = dx Solve y? %3D

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Q: (the trace of A). Prove that T is a linear transformation. Let A and B be to matrices in M, and let…

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Q: Given two planes, discuss the various possibilities for the set of points they have in common. Then…

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Q: Find an equation of the plane that passes through the points (2, 4, 1), (2,2, –4), and (-–3,5, 3).…

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Q: С. lim х-2 х+1

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Q: sin 3x 22. Integrate: JS dx V25-cos² 3x A. -sin-1 (os*) + C 'cos3x' (cos 3x` C. -sin *) + C 15 B.…

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Q: (6) At the start, an experiment records 1 gram of bacterial culture, and the culture's weight is…

A: Given: The initial amount of bacteria i.e. at t=0 hours = 1gm The culture's weight carrying capacity…

Q: Evaluate the limit. t3 + 13 sin (t) lim (Give an exact answer. Use symbolic notation and fractions…

A: The objective of the question is evaluate the limit of the given function.

Q: (cof 5X + CSC 5Xdx

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Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

A: We need to find directional derivative.

Q: The figure shows the stress-strain curve for a material. The scale of the stress axis is set by s =…

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Q: The function f(x) = x + eª has one real zero x0. In which of the following intervals must xo lie? А.…

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Q: Given the graph of y=f(x) below, at which of the marked x-values can the following statements be…

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Q: 0,81 - 0.3104 + 27, wheret is the time in hours after When a factory operates from 6 AM to 6 PM, its…

A: Given problem:- When a factory operates from 6 AM to 6 PM, its total fuel consumption varies…

Q: 14. Which of the situations below could – 100(+7)? A plane, currently flying at an alti A plane,…

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Q: Suppose f( – 1) =7, f'(– 1) = 4 , and g(x) = r°f(x). The tangent line to g(r) at z = 1 is given by Y…

A: Given: gx=x3fx, f-1=7, f'-1=4   The expression for the equation of the tangent line is: y-y0=mx-x0…