12 Give the properties for the equation 9x 2 + 16y 2 - 36x + 96y + 36 = 0 Domain -6 ≤ x ≤ 7 -7 ≤ x ≤ 1 -2 ≤ x ≤ 6

Q: Find the arc length L of the graph of r(t). L = r(t) = 10 cos(t)i + 10 sin(t)j + tk, 0≤t≤ 2π

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Q: graph each function using transformations or the method of key points. Be sure to label key points…

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Q: Find the arc length of the graph of r(t) = ev NOTE: Enter the exact answer. L = 451 e√²ti + e-√² +…

A: Here we have to find the arc length of the graph of r(t)=e√2ti+e-√2tj+2tk , 0<=t<=√2ln5.

Q: π/4 x³ dx (x²+4)5/2 (Use trigonometric substitution)

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Q: (D4 − 1)y = 0

A: D4-1y=0

Q: Given: (1+2x) e-x dx. Using integration by parts and letting u = -1- 2x, dv = f(x)dx, then the value…

A: Let's find.

Q: Using trigonometric substitution, what is √x²-9dx ? f x3 A sec (-) √x²_9 6x² +C B ¹ (1) - V +C (ⒸC)…

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Q: 12. lim [ln(t) sin(t)] t→0+

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Q: Find the partial derivatives of f(x, y) = x³y²

A: Solution ) f(x ,y ) = x3 y2 a) Partial differentiation with respect to x  fx( x ,y ) = 3x2y2 [ y is…

Q: Question 9 A phone company charges for service according to the formula: C(n) = 22 +0.07n, where n…

A: A phone company charges for service according to given function .     [ C(n)= 22 + 0.07n ] Where,…

Q: Use the formula к(t) : = ||r′(t) × r"(t)|| ||r' (t)||³ 9t r(t) = e⁹ti + e-tj to find k(t).

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Q: Solve the initial value problem y' = 4 cos(4x) 3+ 2y , y(0) = -1 and determine where the solution…

A: Given IVP y'=4cos (4x)3+2y , y(0)=-1

Q: Given the function C(a) = (x-4) (x + 6) (x - 1) its C-intercept is its x-intercepts are

A: Solution is given below:

Q: Describe the long run behavior of f(x) AS I→ ∞, f(x) → ? v As → ∞o, f(x) → ? ✓ || H 2³

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Q: Find the solution of the given initial value problem in explicit form. Determine the interval in…

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Q: 49-52 Sketch the curve and find the total area between the curve and the given interval on the…

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Q: 17. 2x√/x dx 18. de xVx S

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Q: Write an equation for a rational function with: Vertical asymptotes at x = 5 and x = -2 x-intercepts…

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Q: Find Do not simplify your answers. dy da 1. log;(√2x² + y) + tan(x² − 7") = sin¯'¹(x² − 1) + ½

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Q: ... : S (1 + 2x) e-x dx. Using integration by parts and letting u = -1- 2x, dv = 2 f(x)dx, then the…

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Q: Give the properties for the equation x 2 +y 2 + 4x + 6y - 12 = 0 Center (4, 6)

A: Given equation of circle is    x 2 +y 2 + 4x + 6y - 12 = 0   Now centre of circle is given by…

Q: Y sinh(1) (use logarithmic differentiation) 3 (sec x)²/2[/cot-¹x]

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Q: x²+x+1 Sa 2x²+2+x³+x² (A (B (D) -b dx dx = [Aƒ (x) – B ln(g(x)]å + D ſb da , and if A = ‚B < 0, then…

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Q: if any. Find the absolute extremum point(s) of f(x) = el-cost on [−5, π],

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Q: d Calculater₁(t) r₂(t)] and [r₁(t) × r₂(t)] first by differentiating dt dt the product directly and…

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Q: Question 2 Consider using the method of partial fractions to solve rb dx = Sa 2x²+2+x³+x² dx = [Aƒ…

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Q: a. Find the volume of the solid obtained by rotating the region bounded by y = x³, y = 8, and x = 0…

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Q: The Leaning Tower of Pisa in Italy is 181 ft tall and makes an angle of 86° with the ground. A…

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Q: Question 6 The IBP formula fudv=uv - fvdu can also be written as fudv+fvdu = uv Which of the…

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Q: Integration of Algebraic Functions By trigonometric Substitution dx 6. S x²√4-x² dx 7. S- √81+x² X…

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Q: A 0 B) 48 32 D) 96 If f cos42t dt = At - B sin 2t cos 2t + D sin 4t cos 4t + C where A, B, C and D…

A: The given problem is solved below in detail.

Q: 18 Identify the center of the conic section whose equation is 5x 2 + 9y 2 - 80x + 54y + 221 = 0…

A: Solution is here

Q: 2. lim (√²-x-√x² + x)

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: domain means value of x which we can put in equation here is in root value cant be less than 0 t -…

Q: VI. Suppose h' is continuous at x = 0 and h'(x) =tan(2x) - 1 if x > 0. Find h(0), if it exists.

A: Let's find.

Q: 15x²x³43x - 19 The integral (x + 1)²(x² - 6x +13) Ax + B What is the value of x²+bx+ca -dx? 3 A…

A: This is a problem related to integration. Based on the concept of partial fraction decomposition we…

Q: Find sets of parametric equations and symmetric equations of the line that passes through the two…

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Q: Find a set of parametric equations of the line through the point (1,-2, 3) and perpendicular to the…

A: Given point(1,-2,3) Then the equation of the line passing through 1,-2,3 is…

Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. (x - 1+1/2/3 1. lim x-1 2x²…

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Q: II. Determine if [x+1]. if x < -1 S x + 1 f(x) = 2 tanh (x+¹) if 1<x< 1 1-x In [cosh (x + 1) + sinh…

A: It is solved whether f(x) is continuous or not.

Q: III. Suppose that a function f(x) satisfies the following properties, together with the table of…

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Q: d d Calculate[r₁(t) r₂(t)] and [r₁(t) × r2(t)] first by differentiating dt the product directly and…

A: This question can be solved using the concept of dot and cross product of two vectors and…

Q: VI. Write TRUE if the statement is correct, otherwise write FALSE. There is no need to justify your…

A: 1. True 2. True

Q: 19. TT/2 -π/2 sin 0 de 20. * sec² 0 de

A: 19 ∫-π/2π/2 sinθdθ [-cosθ ]-π/2π/2 0 - 0 =0 other way sin is odd function so also integration is = 0…

Q: d (h) (cot ¹(2)) = d (i)=(sec ¹(1))= = d (j) (csc-¹(2)) = dr 1 du 1+² dz 1 du I√²-1 dz 1 du I√²-1 dr

A: Given problem:-

Q: Use geometry to evaluate f(2x+5)dx

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Q: Consider the quadratic function f(z) - 2² +0z + 4. Determine the following: (enter all numerical…

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Q: NASA launches a rocket at t=0 seconds. Its height, in meters above sea-level, as a function of time…

A: Given; h(t)=-4.9t2+91t+164

Q: 1. 2. 3. 4. 5. Stan² z dr cot cot2 r dr COS I da sin² x 2 COST da sin r 1₁ sin a cos² x + z] dz 6.…

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Q: Problem 4 The helix r(t) = (cos(xt/2), sin(xt/2), t) intersects the sphere x2 + y² + z² = 2 in two…

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