Replace the Cartesian equation with an equivalent polar equation. x² y² 4 + = 1 49 The equivalent polar equation is (Type an equation using r and 0 as the variables. Type an exact answer, using as needed.)

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

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Q: 2. Fe²i+yj + x²yk, A. y²i2zy2j-e²k B. x²i2y2j-e²j C. y²i2z2j- e²k D. z²i2zy²j+e²k E. y²i-zy2j- e²k…

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Q: Find an equation for the ellipse whose graph is shown. I X y X 3 0 4

A: The figure of the ellipse is To evaluate: The equation of ellipse.

Q: 3x

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Q: Find the principal unit normal vector to the curve at the specified value of the parameter. r(t) =…

A: Given: r(t)=t i+6ti

Q: 1. lim x→-1 2. lim x →-00 1+ x 2x²+x-1 :-√√x² √√x² + x x- 2 x - x

A: Given:     limx→ -11+1x32x2+x-1

Q: Find the point of intersection (xo, Yo, Zo) of the lines given as: o = i i i Vo = Zo = L₁: x= 7+t, y…

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Q: [w (1-32)] 3w 11. lim w In 1 In W→∞

A: LetL=limw→∞ wln1-23wFor L hospital L=limw→∞ ln1-23w1wNow apply L hospital ruleL=limw→∞…

Q: Find all Max., Min., Saddle point for the functions below: P(x) = 2xy-5x²-29² + 4x +49-4

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Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 1. lim 1+1/3 x-12x²+x-1

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Q: mposition =

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Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. (x-3) tan(9-x²) 3. lim x-3…

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Q: Find the volumes for the following solids whose heights are defined by Z(x,y) and bases are the…

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Q: lim (√²-x-√√² + x) H418

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Q: PERFORMANCE STANDARD: Formulate and solve accurately situational problems involving limits. GOAL:…

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Q: Use the information to find and compare Ay and dy. (Round your answers to three decimal places.) y =…

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Q: 7. Do as indicated. 1 1. Let f(x)= = Find the equation of the tangent line to the graph of f'(x) at…

A: This question is related to straight lines, we will solve it using given information.

Q: y"+9y=2e³x

A: Given; y''+9y=2e3x So, we can also write as; D2+9y=2e3x So, the auxiliary equation is; m2+9=0

Q: Find sin (θ) given that cos (θ) = 1/5 and θ is in quadrant IV.

A: Given that  cosθ = 15 and θ is in quadrant IV. We have to find the value of  sinθ.

Q: 7- Differentiate Y= f(g(x4)) h³(√x)

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Q: [2 If A = 3 4 1. 3 2. 6 3. 8 4. 0 x-3 -2 -1 x-27 -1 -5 is a symmetric matrix then x 4

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Q: 6. y" - 4y' + 5y = 4e³t; y(0) = 2, y'(0) = 7

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Q: Find an equation of the plane with the given characteristics. The plane passes through the point (1,…

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

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Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i, j…

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Q: Integrating Factor by Inspection: 7. xdx + ydd = (x² + y²)dx

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Q: Find the value of x + y, if 1. 4 2. 1 3. -3 4 6 [2x 7 5 -y = [8 7 3 D

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Q: How many outcomes are in the sample space if a coin is flipped three times? 8 9 6

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Q: Find the centroid of the given region. (A) (5,15) (B) (3/22,45/61) (C) (5/14,38/35) (8/23,76/111)…

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Q: V. Given: 2. Find f'(2), if it exists. f(x) = el32-61-2, [2x - 5], √x²-9, if x 3 14

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = 2x² - 2 dy= Need Help? Read…

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Q: If y=7x²y+z³ +yz² A = y³ z² e^5x a_x + 4x4 zcosy a_y+ 2x4 CosySinz a_z. Find the following at point…

A: Given, ψ=7x2y+z3+yz2A=y3z2e5x ax+4x4z cosy ay+2x4cosy sinz az           Note: The expert is supposed…

Q: V. Find the slope of the normal line to the graph of g(x) = where x = 0. log₂ (1-x) sin ¹(x) + e² at…

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Q: Solve the given differential equation. All solutions should be found. (4y³ + 2x²y) dx - (3xy² + x³)…

A: Use the substitution method and solve the differential equation.

Q: Integrate the following functions f(x₁y) = (x-1) =x over the given regions y=x²

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Q: Find the curvature and the radius of curvature at the stated point. π r(t) = 10…

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Q: a. (7+7i)(i + 1) UNA 7+7i i+1 C. (727°) (121°) e b.

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Q: Find A where R is the region R outside the circle and inside the V=2 Curve r= 4 Sing

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Q: Replace the Cartesian equation with an equivalent polar equation. x² + y² = 100 Or-10 sin 0 Or- 10…

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Q: Graph the pair of parametric equations with the aid of a graphing calculator. (Hint: don't forget to…

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Q: A courier service will deliver a package only if the length plus girth does not exceed 108 inches.…

A: Use the application of derivative and find the maximum volume.

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: Use the formula k(t): 390 t¹1 k(t) (4 +225 +26) = ||r' (t) x r"(t)|| ||r' (t)||³ r(t) = t²i+t¹5j X…

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Q: Find the particular solution of the  differential equation with the initial condition given below.…

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Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 3. lim (x-3) tan(9-x²)…

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Q: y = x² + 2 Δy = dy= Need Help? x = -3 Read It Ax dx = 0.01 Watch It (Round your answers to four…

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Q: ://v². dx √1-x² dx √√2. x√x²-1 (ª (¹² - 31/₁) dr (1. 25. 27. 29.

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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…

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Q: Determine the values of r for which the differential equation y' +9y = 0 has solutions of the form y…

A: Given differential equation.

Q: Find dy/dx

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