QUESTION 9 Eliminate the parameter to find a Cartesian equation of the curve. x = e²¹ - 1, y = 4f

Q: The graph of g consists of two straight lines and a semicircle as shown in the figure. y 20 y = g(x)…

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Q: 1. Several statements about the definite integral of a continuous function f(x) over [a, b] are…

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Q: Let f(x) = 3x5 - 5x³.

A: The given function,   f(x)=3x5-5x3

Q: 1. If z = f(x, y) has continuous second-order partial derivatives and x = r cos 0, y = r sin 0,…

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Q: Find the indefinite integral. (Use C for the constant of integration.) I Sil sin 20 de

A: 2θ=tdθ=dt2I=12∫ sin4t  dtI=12 ∫ sin t sin3t dt =12∫ 3sint -sin3t4sint dx=38∫ sin2t dt-18∫sin3t sint…

Q: Find the standard form of the equation of the circle having the following properties: Center at the…

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Q: a. Find the other functions of the triangle ABC, given that: 1. Sec A = 2 2. Cot A = 5/2

A: Solution is done in step 2

Q: A point is moving along the graph of the equation y = -5x². At what rate is y changing when x = 2…

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Q: Find the area of the region enclosed by the inner loop of the limaçon r = 13 + 26 cos 0. [Hint: r ≤…

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Q: Consider the function g defined as g(x) = { Evaluate the following limits. 1.) lim g(x) 3x+2 X-2…

A: limit of a function f(x) at a point x=a exists iff limx→a-f(x)=limx→a+f(x)

Q: 2. Using the graph and its labeled points shown below, calculate the Left Riemann sum over the…

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Q: Use the method of cylindrical shells to find the volume V generated by rotating the region bounded…

A: We want to find volume using shells method.

Q: Determine whether each of the following series converges. (Make sure to state which test you are…

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Q: X 75 ft 0 A pole stands 75 feet tall. An angle is formed when wires of various lengths of a feet are…

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Q: 7) Two ships are leaving port at the same time. The first ship sails due east at 20 km/h, the second…

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Q: 7- Differentiate Y= f(g(x*)) h3(Vx)

A: Follow next step

Q: A pendulum of length 10 cm has swung so is radian measure of the angle formed by the pendulum and a…

A: Follow the procedure given below.

Q: ∫12v (7+6v2)9 dv Evaluate indefinite anti-differentiation

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Q: Find the surface area of the region that comes from rotating the given curve about the x-axis: x = 4…

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Q: ∫(x2+5)2 dx Evaluate indefinite anti-differentiation

A: Let's find.

Q: Evaluate the line integral [39a²³yzds with respect to s along the 2 curve C: x = t, y t, y = t²,₁…

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Q: Find the area bounded by the given curves. y = x2 − 1 and y = 8 − 8x2        square units

A: Given :

Q: Solve (5 + x²) Y 1 dy dx = x, and verify your solution. *+C Preview

A: Derivative

Q: Use the graph of g(t) = G'(t) below to answer the following. Make sure to show work and justify your…

A: Area above x axis is positive  are below x axis is negative ∫02 gt dt  = area from 0 to 2=16∫24 gt…

Q: The Smith's borrow $45,000 to purchase a new home. They finance the amount through a 25-yr mortgage…

A: Given problems:- 1. The Smith's borrow $45.000 to purchase a new home. They finance the amount…

Q: sec7(t) tan(t) dt Evaluate indefinite anti-differen

A: We have to find the integral

Q: Two years ago, $5, 000.00 was placed into an investment in which the amount of money present, P,…

A: To find the amount of investment after 15 years from now.

Q: Consider the solid torus (the donut-shaped solid shown in the figure) with radii 5r and 6R. a = 6 b…

A: We have to find the integral and volume.

Q: An airplane leaves City A and flies 144 km due north to City B. It then turns through an angle of…

A: The solution is given in the next step.

Q: Let R be the region bounded by y = sin x, y = 0 and x = with 0≤x≤. Find the centroid of R.

A: The centroid of the region: A region's center of mass, also known as its centroid, is the point at…

Q: 2. Given the first 5 terms below, write down the general term of the following sequences: (a) 80,…

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Q: Let y = 2x². Find the change in y, Ay when I = 4 and Ar 0.1 Sesse Find the differential dy when = 4…

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Q: 8) A rectangle has a perimeter of 8 inches. What should be the dimensions so that its area is a…

A: Given query is to find the dimensions for maximum area.

Q: Decide if the limit exists. If it exists, find it. x²-25 a. lim b. lim X-5 x+5 x²-36 x-5 x-5

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Q: 2. Given the function f(x) = 2x² + 3x + 1, a. Use the secant method to find the instantaneous rate…

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Q: After the release of radioactive material into the atmosphere from a nuclear power plant in a…

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Q: A farmer uses x lb of fertilizer per acre at a cost of $0.20 per pound, leading to a revenue of R =…

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Q: Find the area of the triangle below. Carry your intermediate computations to at least four decimal…

A: Using herons formula

Q: ompute the surface integral over the given ented surface: = y'i + 7j - xk, portion of the plane - 1…

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Q: Rewrite the following series using the E-notation. 1 1 1 1 1 + + + + + + 10 17 26 37 12

A: Solving

Q: Find the particular solution to the differential equation. 2233 Y and y = 4 when x = 0. y(x) = DNE *…

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Q: For the right triangles below, find the exact values of the side lengths b and c. If necessary,…

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Q: Given the functions: Find: f(x) = 3x - 5 a. f(g(x)) g(x) = x² + 2x - 1 b. (f(h(x)) c. f(g(-1)) h(x)…

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Q: Calculate[r₁(t) · r₂(t)] and [r₁(t) × r2(t)] first by differentiating dt he product directly and…

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Q: Assume that x and y are differentiable functions of t. For the following, find dx/dt given that x =…

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Q: 3 5) S² x ² + 1 dx X+1

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Q: f= 1 √√x² + y² + z² 13. Find Vf if 14. If the angle between A = xã, + â andB = V3â, +ây is 60°, find…

A: Given function           f   =1x2+y2+z2 = x2+y2+z2-12       now   we know that       ∇f  =…

Q: Let F(x) = f(x¹) and G(x) = (ƒ(x))ª . You also know that a³ = 14, ƒ(a) = 3, ƒ'(a) = 12, ƒ' (aª) =…

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Q: a graphing utility to construct a table of values for the function. Round your answer to two deci H…

A: Given query is to find the table using graphic utility.

Q: Use Green's Theorem to evaluate the integral. Assume that the curve C' is oriented counterclockwise.…

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