Without using a calculator, for the following, sketch the graph of the polar equation and identify any symmetry: r = 3 cos

Q: 1) (. B enclosed by the curves Find the exact area of the region y=x² and y=x+ 20. Write your answer…

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Q: please both

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Q: egral f x²+x+2 dx (x-1)(x²+5)

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Q: The value of the integral is equal to: Select one: O 4 O с صرا من م من ته 3 x ²² (4x - 4y) dy dx

A: The given integral is: I=∫01∫0x4x-4ydydx   As we know the Power rule: ∫xndx=xn+1n+1+C

Q: Q1 (2 Let R be the region bounded by y = 0, y = x², x = 1. a) [ 1 Sketch the region R. b) Evaluate…

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Q: Find the lim inf (xn) and lim sup (xn) of Xn = √1 + n² 2n - 5

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Q: a) Determine if the geometric series 8-1 gn+1 Σ n= is convergent or not, and find its sum if it is…

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Q: Evaluate the integral 2-x 2 [²² 0 0 xdydx.

A: Solve the integral ∫02 ∫02-x x dy dx. Concept used; Power rule of integration; ∫xndx=xn+1n+1+c

Q: Choose the value of the iterated double integral 1=₁6ydxdy. 0 0-2 O -1 0 1 I 02 O None of the others

A: This question is based on double integration.

Q: Evaluate F F. dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to…

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Q: How many critical points the following function has, f(x, y) = 4x² - 2xy + 2y³? Select one: 0 2 O 0…

A: The given function is: f(x,y)=4x2-2xy+2y3

Q: Find the volume bounded by 3x+2y+z=12 bounded by x=0, y=0, z=0

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Q: Given the function f(x, y) = 2-x² + 2x² - y² a. Find the critical points of f, and determine which…

A: Maxima minima, directional derivative

Q: The shape of a colony of bacteria on a Petri dish is circular. Find the approximate increase in its…

A: topic- application of derivatives

Q: 6. Find the area of one loop of the polar curve r = 2 sin 30

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Q: ƒ7 In ()dx if sec¹ (3x) dx

A: Integration by parts: ∫f(x)·g(x) dx = f(x)·∫g(x) dx - ∫ddxf(x)·∫g(x) dx dx

Q: t: It F is conservative, the integration may be F(x, y) = yi - xj (a) r₂(t) = ti + tj, ost≤1 (b)…

A: Follow the procedure given below.

Q: Use the double integration find the area of the parallelogram whose vertices are A(1,0), B(3,1),…

A: Area of parallelogram

Q: Graph the function by first finding the relative extrema. 1) f(x) = x3+4x2-x-4 24 20 16 12 8 28 55 8…

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Q: The values of two functions, f and g, are given in a table. One, both, or neither of them may be…

A: Solution is given below:

Q: Use the Law of Cosines to find the remaining side(s) and angle(s) if possible. (If not possible…

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Q: The Cartesian coordinates of a point are given. (a) (-6, 6) Find the following values for the polar…

A: Polar coordinates

Q: = Find the area A of the region that is bounded between the curve f(x) = ln (x) + 1 and the line…

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Q: Use the Laplace transform to solve the given initial-value problem. y + 4yet, y(0) - 2 Step 1 To use…

A: By using the Laplace transform to solve the given initial‐value problem.y'+4y=e3t, y0=2

Q: Find y' and the slope of the tangent line to the graph of (2x - 5y)7 = 3y2 -2 at the point (3,1).…

A: The used formulas are

Q: Question 3. (a) (b 2 1 0 -1 Evaluate the determinant of the matrix -1 1 Use the Cramer's rule to…

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Q: Question correct for the series : Which of the following is Σ n=1 Select one: O equals 4. O None of…

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Q: How many critical points the following function has, g(x, y) = x³ + x + xy²? Select one: CO None of…

A: Using partial derivative with respect to x and y ,

Q: Find the antiderivative F of f that satisfies the given condition. Check your answer by comparing…

A: Please see the below picture for detailed solution.

Q: The values of two functions, f and g, are given in a table. One, both, or neither of them may be…

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Q: 4. A certain computer algorithm used to solve very complicated differential equations uses an…

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Q: Find c if a=3mi, b=3.5 mi and ∠C=40.2degrees. c=   mi;

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Q: 3) A) E B) [ Consider the homogeneous DE: y'"" + 2y" + y = 0 Verify that y = cos(x) is a solution of…

A: The given differential equation is;  y''''+2y''+y=0

Q: How many critical points the following function has, h(x, y) = 1 + x³ + x + xy²? Select one: O None…

A: We can find the answer as below.

Q: Question 1 1 a. [ Use the method of Lagrange multipliers to find the extreme value(s) of f(x, y) =…

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Q: 10. Find a Maclaurin series which represents cos(x) for every real number around the point a = 0.

A: As we know the Maclaurin series;  fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+fiva4!x-a4..... Where…

Q: Change the Cartesian integral to an equivalent polar integral, and then evaluate. (9-x2 3 s S - 3…

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Q: The Integral f f 1- y² dxdy is equal to: Select one: O None of them O оос 13 23 1|23|2

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Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. x3 (3x²+2)³ J…

A: Given: I=∫x33x4+23dx     ...1   As we know that; The Power Rule: ∫xndx=xn+1n+1+C ; n≠-1

Q: Let y₁ = e³x and y2 = xe³x be solutions for a homogeneous DE. Then, is also a solution to the DE.…

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Q: Find the absolute maximum and absolute minimum values of the function, if they exist, on the…

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Q: Which of the following is the directional derivative of f(x, y) = 2xy² - x³y at the point (1, 1) in…

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Q: Evaluate the integral given below. Check your answer by differentiating. NOTE: Enter the exact…

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Q: Solve the following equation. [Hint: Change log 4x to base 2.] log2 (x+4) - log 4x=2

A: To solve the equation.

Q: a) [ : Find the volume of the solid obtained by rotating the region bounded by the lines <<math y =…

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Q: Find an equation for the ellipse that satisfies the given conditions. Length of major axis: 10,…

A: NOTE: Refresh your page if you can't see any equations. . here foci n y-axis, which means the…

Q: Evaluate: lim- A. 1 B. e C. 0 D. DNE E. ∞ →2+ [(x² − 4) (-2)]

A: We know, ln(ab)=b*ln(a)

Q: Find the relative extrema of the function and classify each as a maximum or minimum. -2)2/3 5) f(x)…

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Q: Current Attempt in Progress Evaluate the integral by applying the following theorems and the power…

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Q: What is the symmetry of f(x) = 2x4 - 5x² +9? Select one: a. odd b. neither O C. even

A: Solution of given question is written in below steps.