1. Evaluate the line integral where C is the half circle x² + y² = 1, y ≥ 0. 1²+y² ds

Q: Find the area enclosed by the ellipse a cos(t), y = b sin(t) with 0 ≤ t ≤ 2.

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Q: et f(x) = 7x and g(x) = 2x² ind the area of the region enclosed by f(x) and g(x). nswer:

A: Given query is to find area of the region enclosed.

Q: Find the arclength of the curve x with 2 ≤ t ≤9. 1 3 Y - 2

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Q: + 4 -1 -3 1dz = -2 given below. -1 2 -1+ Q the limit definition of the definite integral to…

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Q: A flat rectangular piece of cardboard of dimensions 6 cm by 10 cm is transformed into an open-top…

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Q: Eliminate the parameter t to find a Cartesian equation in the form x = f(y) for: [x(t): 2+² ly(t) =…

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Q: 2. xy + y = (xy) ³/nx

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Q: 13. Find the domain, range, and right end behavior (xx) of each function below: (a) f(x) = -2(1.3)…

A: We know an exponential function is valid for all real number and it gives always positive real…

Q: Let f(x) be defined such that f(2)= 3 and f'(x) = cos(+x), where 1 < x < 4. Part A: Find the tangent…

A: Please see the below picture for detailed solution.

Q: Given the parametric equations below, eliminate the parameter t to obtain an equation for y as a…

A: To find y in terms of x  first find t from x(t) and then substitute the value of t in y(t).

Q: The solution of the D.E. xdy - ydx = x² + y²dx is 2 a. y-√√x² + y² = cx² O (a). c. y+√√x² + y² + cx²…

A: Given: xdy-ydx=x2+y2dx

Q: Evaluate. 5 -1 -1 (4x²-3x+5) dx (4x²-3x+5) dx = (Type an exact answer in simplified form.) ***

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Q: Sketch a graph of a = 1 + cos(t), y = 2 + sin(t), 0 < t < 27 . -5 -4 -3 -2 -1 Clear All Draw: 6. 4-…

A: Please see the below picture for detailed solution.

Q: 3 (cos (4) + 4 sin (4) 3 3 z=3

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Q: Given: f(x, y) = x³y +exy² find fxy to 9. b. find a³f хепеле

A: Given f(x,y)=x3y+exy2

Q: dt If an amount Po is invested in the Mandelbrot Bond Fund and interest is compounded continuously…

A: Given that the interest is compounded continuously at 6.8% per year, the balance P grows at the rate…

Q: Solve the differential equation. FD dy dx 3e * y = 2, x > 0

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Q: A microbial population's mass grows in such a way that its rate of growth r(t) = m(t) doubles every…

A: A microbial population's mass grows in such a way that its rate of growth r(t)= m'(t) doubles…

Q: Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit.…

A: We have to find if the given series convergent or divergent.

Q: Find the indicated partial derivative: Y Ə dy y + 2x = [

A: Given query is to find the partial derivative.

Q: At OHaganBooks.com, the rate of net sales (sales minus returns) of The Secret Loves of John O, a…

A: NOTE: Refresh your page if you can't see any equations. . the rate of net sales is given by where…

Q: Coefficients Linear in two variables. Find a general solution of the differential equation (y - 4x -…

A: We know  ∫xdx/(x²+1)= (ln|x²+1|)/2  ∫dx/(x²+1)= tan-1(x) or arctan(x) Given differential equation,…

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = √16 - x² dy =

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Q: and and simplify the expression and yd Booze (Cos+isin)³ ress the answer in standard form, a + bi.

A: Given query is to find the a+ib form.

Q: h(t) = 4e5t-7t-3 Determine the value of h'(-1).

A: Given query is to find indicated derivative.

Q: 3. Find the volume of the curve x² = 4y and the line x = y rotated about the x-axis.

A: Note: As per our guidelines, I have solved one (Question number 3) problem. If you want the solution…

Q: If csc(x)=8, for 90∘<x<180, then sin(x/2)=___ cos(x/2)=___ tan(x/2)=_

A: SOLUTION-

Q: If f(x) = [² cos(t)dt then f'(x) =

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: dy dx x = h - 2 x (1 - y = x² sin x

A: xdydx-y=x2sinxdydx-1xy=xsinxthis is linear differential queation of first order

Q: Suppose f(x, y) = x²y + 6. Compute the following quantities: f(0, 0) f(4, -3) • f(-3, 4) . . = =…

A: NOTE: Refresh your page if you can't see any equations. . substitute (x,y)=(0,0)

Q: 1) Consider the functions ƒ(a) = 100 – 2¹ª and F(x) = f(t 1² f(t) dt. i. Write a simplified form of…

A: As per Bartleby guidelines we only give first question answers. Please repost for other parts.

Q: 12. A laptop computer was purchased for $2500. After 2 years, the value of the laptop is expected to…

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Q: Use sigma notation to write the sum. 1 5(4) Σ i = 1 + 2 5(5) + 3 5(6) + + 10 5(13)

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Q: Answer the following questions about the function whose derivative is given below. a. What are the…

A: The first derivative is given by: f'x=sinx+cosxsinx-cosx For critical points, we will put the first…

Q: 11. Suppose the population of a town is 23,000 people in 2010. Write an equation for the population…

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Q: The marginal revenue derived from producing q units of a certain product is given by R'(q) dollars…

A: To solve the following problem

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 3'(x) =…

A: NOTE: Refresh your page if you can't see any equations. . use the fundamental theorem of calculus

Q: a. Find the open interval(s) on which the function is increasing and decreasing. b. Identify the…

A: We have to find the critical points and absolute extrema.

Q: find the average vaim of the function fcx) = x² = 5x + 6 cosx on th Interval [-1, [-1,3].

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Q: 6.) so +3 dx 2xe+²+

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Q: If cot(x)=8/11 (in Quadrant-I), find cos(2x) = ------ (Please enter answer accurate to 4 decimal…

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Q: The bearing from city A to city B is S 20°E and the bearing from city B to city C is N 55°E. (See…

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Q: Find a) any critical values and b) any relative extrema. f(x)=x²-6x+5

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Q: Find the accumulated present value of a continuous stream of income at rate R(= $136,000, for time…

A: Given: Initial value=$136000 Time= 17 years  Interest rate k=7%

Q: In 2000 the population of a country reached 1 billion, and in 2025 it is projected to be 1.4…

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Q: home owner installs a solar heating system, which is expected to generate savings at the rate of…

A: Given query is to find the formula for total savings in t year.

Q: Evaluate the geometric series or state that it diverges. 8 Σe-2n n=0 Select the correct choice below…

A: Given sereis:- ∑n=0∞e-2n

Q: Find the rate of change of total revenue, cost, and profit with respect to time. Assume that R(x)…

A: To find the rate of change of total revenue, cost, and profit with respect to time. Assume that Rx…

Q: gradient of the line joining the points (3, 5) and (2, 8) is

A: Given query is to find the gradient of the line.

Q: At OHaganBooks.com, the rate of net sales (sales minus returns) of The Secret Loves of John O, a…

A: To solve the following problem