Convert the polar equation T = y = 2 r² sin³ (0) - 7 cos(0) into a cartesian equation, and solve for y.

Q: The daily marginal revenue function is R'(x) = -0.02x + 8 unit per where R'(x) is measured in…

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Q: show work.

A: 18)  Graph of the function is shown below

Q: Consider the vector field F = S.F Evaluate F. dr along the curve C: π r(t) = 2 cos(t)i +2 sin(t)j,…

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Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5) 2=2y the…

A: The area of the smaller region( to the left of the parabola) bounded by  the x-axis, and the tangent…

Q: A: The plane Ax - By + Cz - 1 = 0 pass through non collinear points (1,1,0), (2,0,-1) and (2,9,2).…

A: Given that the plane  passes through non collinear points

Q: Suppose that ♬ = 5x²/5 + ev/²3, and let C be the path consisting of (i) an arc along y = x² - 1 from…

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Q: Estimate the area under the graph of f(x) = 49-² over the interval [-2, 6] using eight approximating…

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Q: > b) find a formula for s„, n ≥ 1. 1/3, 2/5, 3/7, 4/9, 5/11, ... 1/2, -1/4, 1/6, -1/8, 1/10,...

A: The series a is given by:- The series b is given by:-

Q: 7. Refer to the following graph of f(x). a. At what value(s) of x is f(x) discontinuous? b.…

A: Types of discontinuity (i) if  then function has  point/removable discontinuity at x=a(ii) if  then…

Q: Find the curve: equation for the tangent line to Y = 8x + ³/² at x = 3

A: y=8x+3x at x=3

Q: a differential equation for the functions 2 A. y = 3x + x² - 4x D Find following е B. y e C. D. y =…

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Q: .  (a) Sketch the graph of y = 2x2 over the interval [-1,1] (b) Let x be any point in the interval…

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Q: Find the following cardinalities: a. A when A= {5, 6, 7, 8, ..., 34}. b. A when A= {x € Z : −6 ≤ x ≤…

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Q: Using separation of variables, solve the differential equation, Use C to represent the arbitrary…

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Q: Find the exact length of the curve. x = 1 + 9t², y = 3 + 6t³, 0≤t≤3

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Q: show work .

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Q: An epidemic spreads through a population at a rate proportional to the product of the number of…

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Q: In many population growth problems, there is an upper limit beyond which the population cannot grow.…

A: The given differential equation is

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

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Q: series. 36 + 12 + 4 + find the sum of the infinite geometric 4 4 + + 3 9 -810 + 540-360+240-160+...

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Q: Determine all critical points for the following function. f(x)=2x(4-x)³ X= (Use a comma to separate…

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Q: 19.fe-2x sinh² 3x dx = =

A: To evaluate the following integral.

Q: 18. Determine the area of the region bounded by y = 2x² +10 and y= 4x+1 below. (Warning: graph not…

A: In the given figure , we can see that point of intersection of these two graph are at x= -1 and x=…

Q: Find the most general antiderivative. √(0²³² + +1) C 61² dt 10

A: Given thatto find antiderivative of the functionusing the formula

Q: (b) Find the rate at which the depth of water is changing when h=10 cm.

A: Given that,vertical height = 25cm, water depth = h cm. From the given figure (a) Since, the volume…

Q: The one-to-one functions g and h are defined as follows. g={(-9, 0), (1, −8), (2, 3), (8, 1)} h(x) =…

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Q: Use linear approximation, i.e. the tangent line, to approximate 18.22 as follows: Let f(x) = x² and…

A: f(x)=x2, x=18Approximate 18.22.

Q: find the general solution (x^2+y^2) dx - xydy = 0

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Q: l fx dx = n+1 T X n+l +C for all n F

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Q: a. Select the correct choice below and fill in the answer boxes to complete your choice. O A. f(x) =…

A: We need to fill in the boxes.

Q: Let f(x) = (9 sin x + 7 cos x) tan¯¹x ƒ'(x) =

A:

Q: π/2 Ă π/4 7x csc²(x) dx

A: To evaluate the following integral.

Q: Given the values of the derivative f'(x) in the table and that f(0) = 175, estimate the values…

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Q: Evaluate the following Riemann sum over interval [0,2] when f(x) = x(2-x). Use regular partitions…

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Q: Evaluate this improper integral and determine whether it is convergent or divergent Se le ¹/x x3…

A: To evaluate the following integral and to determine whether it is convergent or divergent.

Q: The table given below shows the Consumer Price Index (CPI) for selected years. Use the regression…

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Q: A force of 30 newtons stretches a spring 0.3 meter from its natural length of 1.5 meters. Find the…

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Q: s ›) decide which of the following are geo- metric series. For those which are, give the first term…

A: The given series are a) 5-10+20-40+80......

Q: Question 1. Let f(x) = (x³ + x² + 1)e ³+1 and g(x) = ex³+1¸ (a) Draw a rough sketch of the graphs of…

A: The given curves are   and

Q: Show the following question with different approaches: limx→∞ (4x − 3 cos(2√(x + 1)))/(5 − 6x)

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Q: Find the area of the region enclosed by the curves y = 8 1+ and y = 4 The area of the region…

A: To find the area of the region enclosed by the curves .

Q: Find the coordinates of a second point on the graph of a function fif the given point graph and the…

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Q: 02.6 Determine the most general real valued solution for the below system of linear differential…

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Q: Solve for x. Round your answer to four decimal places. log (base4)x+ log (base4)( x + 4) = 8

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Q: Which one of the following Riemann sums approximates (10 + dx using 4 skubintervals X of equal…

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Q: (a) (b) 12 in (1 + √5) In 3 In 2 (c) (24) (d) - In (1+√3) =)/In (1+ √5) √ √2+1 dx = ? In 2+√3

A: The given integral is

Q: What is √(x²-3) (x5_4) dx ?

A: Given Indefinite Integral As we know that

Q: Let (-5, -7) be a point on the terminal side of 0. Find the exact values of sin0, sece, and tan 0.…

A: The given point is (-5,-7).Find sin(theta), sec(theta), tan(theta).

Q: 2 Find the ZZ=1 and чу Find the curvature of the curve F(t) = (t, 3 cost, 3 sint 0 -

A: To find the curvature of the curve .

Q: 1.2 Find the domain and range for f(x) = √4 − 2x + 5

A: f(x)=4−2x+5