Homework 12 Polar: Problem 6 Find the area enclosed by one loop of the lemniscate with equation ² = 64 cos 20 shown in the figure. Choose your limits of integration carefully. With ro = 8 Answer: Fo X

Q: Match the function with one of the graphs below using horizontal asymptotes as an aid. f(x) = 5+ H…

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Q: Write the Taylor series for f(x) = xº about x = −4 as Σ Cn (x + 4)". n=0 Find the first five…

A: The given function is  f(x)=x3 about x=-4.

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: Evaluate the following limits. USE OF L'HOPITAL'S RULE IS NOT ALLOWED. 3. lim (x-3) tan(9-x²) sin²…

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Q: Find all solutions of the equation in the interval [0, 21). csc 0 7 3 If there is more than one…

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Q: 2. Show that F is a conservative vector field and then use that fact to evaluate SF. dr along the…

A: We need to show F is conservative vector field.

Q: Integrating 1. y' + y = x+ Factor by Linear Equations:

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Q: Given a sin 6t and y = cos 6t, find the following derivatives as functions of t. dy/da 1 d'y/dx² =

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Q: Solve for the solution of: (D3 + D)2y = 0

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Q: A metal plug has been designed using the intersection of the two cones z = √√x² + y² and √x² + y² +…

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Q: Write TRUE if the statement is correct, otherwise write FALSE. y y = h'(x) (-3,0) (3,0) x (-1,-2)…

A: To write TRUE if the statement is correct, otherwise to write FALSE. Suppose that hx is continuous…

Q: Find the exact length. T=0², 0≤0 ≤ 2π ° 4[G²+1²] ²3 [(x² + 1)² - 1] [(²+1)-1] ° 4[68² +1²]

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Q: Cheyenne, Wyoming, has a latitude of 41° N. At this latitude, the number of hours of daylight D can…

A: Given :  D = 2.914 sin(0.017t 1.321) + 12.134

Q: what values of x is f(x) = 2 tan(x + π/6) discontinuous?

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

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Q: 8 sin 8. Then sketch the curve.

A: The correct curve of r = 8 -8sin(θ) is  Option (C)

Q: 6. Use Green's Theorem to find the counterclockwise circulation and the outward flux for the field F…

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Q: Integrating Factor by Linear Equations: 5.y' = 1-2y cot2x

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Q: Verify Green's Theorem by evaluating both integrals dA [_v² dx + x² dy = [] (ON-OM) A ax ay for the…

A: Let's find.

Q: Match the vector field with its graph. F(x, y) = yi 址 四 場 x Q 6 電

A: F(x,y)=yi So at any point vector magnitude is same as y-cooridnate Also, if y is negative [below the…

Q: The function f is defined by f(x) = -2x³ - x² - 6x and the point (-1,7) is on the graph of f. If f¹…

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Q: . DO NOT SIMPLIFY YOUR ANSWERS. - 1. log₂ 19²( √/2x² + y) + tan(x² − x²) = sin^¹(x² − 1) + ² Find d

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Q: Find the Cartesian coordinates of the given point. (-4, -1/3) ○ (-2,2-√√3) (2,2-√√3) (-2-√√/3,-2) Ⓒ…

A: First I have written the Cartesian coordinates of a polar coordinates rule, just use it for given…

Q: Write the Taylor series for f(x) = sin(x) at x = Find the first five coefficients. Co C₁= C2= C3=…

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = -2x - (sin(x))² dy = X Read…

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Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with…

A: Find u+v

Q: Find a power series representation for the function. (Give your power series representation centered…

A: We have to find the Power series representation.

Q: Ex. (9) Solve 3y"-2y' + y = 4x+2

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Q: A fence is to be built to enclose a rectangular area of 240 square feet. The fence along three sides…

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Q: Solve the following differential equations of d² y dx² dx dy +3 dv −10y=3x²

A: We have to find the solution of the given differential equation.

Q: Find the Maclaurin series centered at c and the interval of convergence. 12) f(x) = 1-2x 13)f(x) =…

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Q: Suppose that f(x) and g(x) are given by the power series f(x) = 3 + 4x + 3x² + 2x³+... and g(x) = 6…

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Q: Apply the Ratio Test to determine convergence or divergence, or state that the Ratio Test is…

A: Here, the given series is: ∑n=1∞7n2(2n+1)! Let, an=7n2(2n+1)!; n≥1

Q: 5 If [F(x) dx f(x) dx = 7.4 and 1.°F(x) dx f(x) dx = 5.7, find [²1 f(x) dx.

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Q: Find all solutions to the equation. csc 0-√2=0 Write your answer in radians in terms of , and use…

A: As we know that; The general solution of the trigonometric equation sinθ=sinα is; θ=kπ+-1kα,  where…

Q: Find the slope of the tangent line to the polar curve r = sin(70) at 0=. Enter as an integer or…

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Q: Consider the function f with the following properties: f is continuous everywhere except at x = 2…

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Q: Assuming that the equations define x and y implicitly as differentiable functions x = f(t), y =…

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Q: 15. Sketch y = f(x). Properties are: Max at P(2, 2) Mins at Q(4, -1), R(-1,2). Oblique asymptote y =…

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Q: Write an equation for the polynomial graphed below y(x) = N w 2 N

A: Here X intercept of the polynomial is x=-2, x=-1, x=1,x=3 and graph just touch x axis at x=1 and…

Q: Consider the function y=x³ - 9x + 4. a. Sketch the graph of y= x³ – 9x + 4. b. Find and describe the…

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Q: Find dy/dx by implicit differentiation. x²y³ -yax dy/dx =

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Q: Find two positive integers such that the sum of the first number and four times the second number is…

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Q: 17 Select the conic section represented by the equation. 4x 2 -y 2 + 24x + 4y + 28 = 0. circle…

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Q: Find the one-sided limit (if it exists). (If the limit does not exist, enter DNE.) 2√x lim CSC X

A: Explained below

Q: fx-²dx

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Q: lim x++∞ COS X log logi x

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Q: Find the nth Maclaurin polynomial for the function. f(x) = ex, n = 5 P5(x) =

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Q: Integrating Factor by Inspection: 3. xdyydx = 3x²(x² + y²)dx

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