Find an equation of the hyperbola that has vertices (0,±6) and foci (0, ±7). Equation: 1

Q: Given x = 84t + 44 and y = (i) dx dt dy dt (ii). = = 1092t² + 115 (iii) dy dx (write the simplified…

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Q: 12. 1111111 Carefully explain, using diagrams and definitions as needed, what a scalar line integral…

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Q: Find the area of the following region. The region inside the curve r = √14 cos 0 and inside the…

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Q: The series n=1 (2n − 1)! (n + 2)! O is absolutely convergent O is conditionally convergent, but not…

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Q: A trapezoid has one of its legs perpendicular to both parallel bases. If the altitude of the…

A: According to question,Given,Height of Trapezoid, H = 3 units.

Q: Estimate the value of 1.011.01 using differentials. O 0.99 O 1.0101 O 0.9899 O 1.01

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Q: dy 18. Obtain general solution of=3√/xy a. 2√y=²√√x³+c c. b. y = 2y√x³ + c 2(√y-√√x²)=c d.…

A: The given differential equation dydx=3xy. We have to find the general solution of the differential…

Q: Given x = 2 sin (17t) + 17 and y = 4 cos(17t) + 143

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Q: For the parametric equations: x = 23et and y (write the number answer only in the box) (i) ii) (iii)…

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Q: 1. ſ(x² + x)(xª + x−¹ + 2)dx

A: We can evaluate the given integral in the below steps.

Q: 1. Assume that 1 mol of gas has the following equation of state: p = RT+b V. Answer the following…

A: as we know for gas equation that R and b is constant so variables are T and V p = RT + bV

Q: 5 - 25 + Z² = -1 2x + 34 = 2 -y-27 = 0 (Mabrices), find of 2 Rom Rescaling

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Q: The small town of Boringville had a population of 5200 in the year 2000. The birth and death rates…

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Q: Estimate the value of log,8.9. O 2- 2+ 2+ 1 90 1 60 ✔ logge -logge - 108 90 1 2- - logge 60

A: The objective of the question is choose the correct option by evaluating.

Q: te a function based on the given parent function and transformations in the give 1 ent function: y=…

A: Given query is to applied indicated transformation.

Q: he following table gives the values of a function f at a certain number of points.  *Table is…

A: we have to evaluate the integral  ∫25f(x)dx (a)  using midpoint rule- here b =5  and a =2     let n…

Q: lim (x,y)→(0,0) COS [y ln(x+1) exy+2

A: The solution is given below

Q: ( ) Given the force field F =, find the work | F. dr required to move an object C on the curve…

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Q: 1. Find the following limits or explain why they do not exist: x² - 2x - 3 x+3x2 – 5x +ổ x² - 2x 2 3…

A: To find the following limits or to explain why they do not exist.a limx→3 x2-2x-3x2-5x+6b limx→2…

Q: x2+2x+5. Show, x+2 Q1 Let f: R\ {-2} → R be given by f(x) directly from the definition, that f is…

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Q: Givenx = (i) (ii) dx dt dy dt - || dy (iii) dx -95 + 114 and y = 95 ln(5t) — 43 (write the…

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Q: Solve the following equations in the interval [0, 2 ]. Note: Give the answer as a multiple of . Do…

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Q: m of linear equations x +y = 3z = 2 2x + 3y + 2 = 0 3x + 4y = 2 =1 using 23 the

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Q: 2. f'(-0.1) -5.84 3. f'(-0.1) -5.74 4. f'(-0.1) -5.64 5. f'(-0.1) ≈ -5.54 (iv) Use p4 to estimate…

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Q: 1. y = csc x + y cot x ; x = 0, y = 2

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Q: Let f(x) = 7x√√/1-x², with domain x € [-1, 1]. Find the area of the region between the curve y =…

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Q: 8. Solve (cos x cos y-cot x) dx -sin x sin y dy = 0 sin x cos y = In (c cos x) a. b. c. sin x cos y…

A: To solve the given differential equation

Q: 7. Given a DE: y" + 2y' - 8y = 0 and a solution of the form y = ex for some (unknown) constant "r".…

A: The objective is to solve the above question.

Q: If f(x): = 0 * sin(x) S V4 + t2 dt and g(y) = = [ f(x) f(x) dx, find g ¹*(17). 6

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Q: Find the first partial derivatives of the following: ∙i. f(x, y) = tan(3x − y) + - ii. g(x, y) = xy…

A: To find the first partial derivatives  of the following:i fx, y=tan3x-y+xyii gx, y=xyiii fx, y,…

Q: A cannon ball is shot into the air such that its height h, in metres, after time t, in seconds, can…

A: Topic = Derivative

Q: Solve for a2f дхдz if f (x, y, z) = x³=3y

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Q: Plot the points with polar coordinates (-5, 2¹) and 3, π 5л 6 71 6 3μ 4 5π 4 2л 3 41 3 EIN π 2 3μ 2…

A: We need to mark given coordinates.

Q: u

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Q: 16 Co C D If u=lnx, then A B [² 1 2 5² 1 So e 2 1- (lnx) (1-u²) du (1-u) du © ²³ (1 - 1²) u ) du e2…

A: The given integral is [1-(ln x)2]/x, limit from e to e2.

Q: Equation y" - 2y + 2y = exsinx (5) (21 2 2 Appropriate Form of the Particular Solution

A: We need to solve Differential equation. As per Bartleby guidelines we can solve one question from…

Q: Sketch the region of integration, reverse the order of integration, and evaluate the integral. X…

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Q: An equation of a parabola is given. y² = -32x (a) Find the focus, directrix, and focal diameter of…

A: To find focus directrix of given parabola.

Q: 12. Which of the following is equation is an exact DE a. (x²+ 1)dx + xydy=0 b. xdy+ (3x-2y) dx = 0…

A: standard form of differential equation M dx + N dy = 0 if ∂M∂y = ∂N∂xthen given DE will be exact

Q: Find the number c which satisfies the conclusion of the Mean Value Theorem for the function f(x)…

A: The given function fx=4x2+2 on the interval -10, 8. We have to find the value of c that satisfies…

Q: x± – 2x – 3 x⇒2 x2 – 5x + 6° - (b) lim

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Q: Blank 1 0 Question 22 . If f'(x) = 4x³ + 3x² + 6x and f(1) = -3, then C = ANSWER: C = Blank 1 Blank…

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Q: 2. yy'-6y = x² + 3x; y(0) = 1, y'(0) = 1

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Q: Use double integration to find the area of the region enclosed by the graphs of y = 5√√x and y = 2.…

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Q: Let f(x) = √√2 x ln(2x - 1). Use the local linear approximation of f(x) at xo = 1 to estimate the…

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Q: Prove that k=2 1 k (Ink)" converges when p > 1 and diverges when p ≤ 1.

A: To prove that ∑k=2∞ 1kln kp converges when p>1 and diverges when p≤1.

Q: Consider the indefinite integral transforms the integral into: 7 Ա ["=3 du u² S= 1 of the du of th 7…

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Q: 4) Find the mean and rms value of the voltage v given by the equation V=45sin(wt)

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Q: Use chain rule to find fss for f(x, y) = 2x + 4xy-y² with x = s + 2t and y = t√√s

A: we have to find   fss     f(x,y)=2x+4xy-y2fs=∂∂s2x+4xy-y2fs=2∂x∂s+4x∂y∂s+4y∂x∂s-2y∂y∂s since ------…

Q: xdy dx - 4y = x6ex

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