Convert the Polar coordinate to the Cartesian coordinate. 1. r= 1+2r cose 2. r=1-cos8

Q: Let the vector v have an initial point at (−3, 4) and a terminal point at (-2, 6). Determine the…

A: NOTE: Refresh your page if you can't see any equations. .

Q: valuate the integ

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Q: A population of birds on an island is initially 380 birds, and it doubles (or grows by 100%) each…

A: It is given that initial population of birds on an island is 380. Each year population of birds gets…

Q: 67. = 2x − 7, y(2) = 0 dy dx dy 68. = 10 - x, y(0) = -1 dx 1 69. dx + x, x > 0; y(2) = 1

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: x² + y² Briefly differentiate directional derivatives with suitable graph and equations.

A: This is a problem related to vector calculus. Based on the general formula and calculation we will…

Q: Set up the integral to find the area of M, using vertical ectangle. Let M be the region bounded by…

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Q: Evaluate the integral. Please show step by step! S sin x 1-2 sin² x cos²x dx

A: I am attaching image so that you understand each and every step.

Q: (b) Show that the function defined by √₂²+y f(x, y) = 0 if (x, y) = (0,0) is not differentiable at…

A: On solving this we will get

Q: 3πt -? What is the value of Sin 4 2. What is the value of Tan 3

A: Given sin3π4            ⇒sin3π4=22=0.707

Q: 4. ABP is a triangle, M is a point on AP. AB = a, AM = 26, and MP = 6. N is the midpoint of BP. C is…

A: We have to find PB→ and prove that M,N and C lie on the same line.

Q: Calculate the area contained between the curve y = cos x, π<x< , and the line y =

A: Given:-y=cosx, -π&lt;x&lt;πy=1/2

Q: 8. 9. 10. Given f(x) = cos(3x + π), find ƒ'(π) a) 0 b) -1 c) -3 If f(x) = √ex, the derivative is: a)…

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Q: Find the area of the surface generated when the given curve is revolved about the x-axis. 3 X 1 1 /=…

A: Given problem:- Find the area of the surface generated when the given curve is revolved about the…

Q: If r(t) = (3t, 2t², 4t³), find r'(t), T(1), r"(t), and r'(t) x r"(t). r' (t) = T(1) = r"(t) = r'(t)…

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Q: Use the following information to answer the next question the graph shown below is obtained by…

A: Please refer to the image below

Q: 10-x-x² if x 5 Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(x) =…

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Q: 7. Find the limit, if it exists. If the limit does not exist, explain why. sin(2x - 6) sin(4x - 12)…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: f (x) = 2x+7 if -5=Xcl 8 If X = 1 14X=3 if 11x-2 31 If x > 3 IS this continuous at X=1 ? formula…

A: Any function f(x) is continuous at x=a if  lim x -&gt; a f(x) = f(a) i.e. Functional value at that…

Q: Differentiate and simplify this function k (t) = e√t^2+t+1 - e-√t^2+t+1

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Q: Question Integrate (three) of the following integrals: 1) f sin6x cos3x dx 2) f x√√x + 1 dx cos2x…

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Q: b) Use chain rule 1 y= LESANNE aretan u where u eª ue

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Q: state whether the following series is convergent or divergent and state which test you used: an =…

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Q: Let the vector v have an initial point at (2, −8) and a terminal point at (−1, −8). Determine the…

A: Let the vector v have an initial point at 2, -8 and a terminal point at -1, -8.To determine the…

Q: Determine the following limit at infinity. lim f(x) X→∞ 9(x) if f(x)→700,000 and g(x)→∞o as x→∞ Find…

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Q: The weekly cost of producing x key chains is given by the function C(x) = 1800 + 33x + 0.15x2. Find…

A: marginal average cost

Q: Question 13 d²2 Which of the following satisfies the differential equation dx² A. y = e³x B.y = e-3x…

A: We need to choose correct option.

Q: √√3+ rdr then 0 (2)=√√3+230 I X

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Q: 5) Calculate the area in square units, bounded by g(x)= 4x+8_and_f(x)=x² +19x+62 over the interval…

A: NOTE: Refresh your page if you can't see any equations. . here we have  and the interval is  so…

Q: Evaluate the following integrals I 1. x² - x 1+3x²2x³ dx J₁ 2. /1+2 I dx 1 + 2 sin r ²+2 3. da x + 1…

A: Note that, according to Bartleby guidelines, we can answer only the first 3 sub-parts in the case of…

Q: Determine the equation of the ellipse with foci (-8, 14) and (-8, -16), and co- vertices (0, -1) and…

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Q: A) 0 B) 3 (C) 2 (D) 4 E 5 F) 1 Use polynomial long division to write 2x² + x³ 3x² + 4x-9 x² + x =…

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Q: Given plane z: 3x+2y+=-3=0, point P(1, -2, 3), and lines 1₁:¹¹ and 4₂: (3, 6,-5)+r(2, 3, 1), find:…

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Q: passes through the point P(3,7,2) and is perpendicular to the plane 3x − 5z – 7 = 0. -

A: The given point is P3,7,2 and the given plane is 3x-5z-7=0.We need to find the vector equation of a…

Q: erivative 263.7 0.5cos0+ 0.3515.sim

A: Derivative

Q: + 1 -оу-х -oy=x2

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Q: Differentiate and simplify this function h (z) = (ez - 1)1/2

A: Given function is: h (z) = (ez - 1)1/2

Q: 27) 5 1 dx √x²- A) in (x+2+25+C In 5+X In +C 10 5-x nt B) +C X+5 D) (x+12-25374c In +C

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Q: 9 The slope of the function ƒ (x) = 8 - 2x is _____. -8 -2 2 8

A: here we have to find the slope of function  so we have to find dy/dx so differentiate the function

Q: Calculate the volume of solid of revolution when the region bounded by y = sin 2x and x² - y2 = 0 is…

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Q: Identify the theorem: If S is the boundary surface of a solid E in 3-dimensional space, then SS, F.…

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Q: Let the vector v have an initial point at (−1, 1) and a terminal point at (5, –5). Plot he vector v…

A: We have to find the component, magnitude and direction of given vector.

Q: Q2: The population of a state is known to grow at a rate proportional to the number of people…

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Q: The function f(x) = 7 1+9x² f(x) = Σ cnan. n=0 Find the first few coefficients in the power corios…

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Q: If 2 = (6,-5) and a = (-2,6), find |2+3.5d |. O 5√11 O √146 O 16 2√73

A: topic- vectors

Q: (D² - 2D+5)y=e* cos x

A: I am attaching image so that you understand each and every step.

Q: Question 13 Which of the following satisfies the differential equation d² y dx² A. y = e³r B.y=e-3x…

A: Explanation of the answer is as follows

Q: 1 B) Find all of the second derivatives for f(x, y) = (3xy² + 2xy + x²) In; x²+y²

A: To find all the second derivatives for fx, y=3xy2+2xy+x2 ln1x2+y2.

Q: sider the function p 3 of 3: Find lim f(x). x--6 f(x) = = lim f(x) x--6 Sx² + 12x + 22 19x + 100 if…

A: Topic:- limit and continuity

Q: Jy Find the area of the inner loop of the curve r = 9 cos 0 - 4 by using double integral.

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Q: 1. Assuming that one of the sides of a rectangular field is along a river bank and no fencing is…

A: In this question, we want to know the dimensions of the rectangular field that will satisfy the…