Find the maximum area of an isosceles triangle inscribed inside the ellipse x²y² 1, + = a² 62 with the triangle's apex (the vertex opposite the base) positioned at x = a.

Q: Find all solutions of the equation in the interval [0, 27). (Enter your answers as a comma-separated…

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Q: 1/2 y = (4x-3)¹/²₂ d³y 3 dx

A: Third derivative id given.

Q: Evaluate the line integral ſ F. dr, where F(x, y, z) = sin x i + cos y j + xz k, where C is given by…

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Q: Graph the pair of parametric equations with the aid of a graphing calculator x = 4 sin t - sin 4t, y…

A: Given x=4sint-sin4ty=4cost-cos4t0≤t≤2π

Q: (b) y=x-6, (1, 1)

A: answer is in next step

Q: Find all solutions of the equation in the interval [0, 27). 2cos’x– cosx−1=0 Write your answer in…

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

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Q: 3. Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that has a…

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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: For the graph below, the concavity switches at x = ±1.7 and 0 and there are critical points at x…

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Q: Find the integral of the following equation integrate cos(x + pi/3) dx

A: Given problem:- Find the integral of the following equation integrate cos(x + pi/3) dx

Q: Direction: Find the integral of the following functions: 1. (5 cos x + 7 sin x) dx 2. f(3tan² x +…

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Q: 27 SECOND DERIVATIVES Find TUTORIAL 22 if y-In (x + 1). Answer 2-2x² 22-2

A: Note:-As per your mentioned request i am solving question 1 from the given figure.

Q: 3. lim x 3 (x-3) tan(9-x²) sin (2x-6)

A: Explanation of the answer is as follows

Q: veen y - II [U, 1].

A: We will find the area .

Q: enclosed by Find the area X = 2y² and x = 8 the сикише

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Q: Complete the table. (Round your answers to four decimal places.) X-7 x-7x²²-8x+7 x 6.9 6.99 6.999 7…

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Q: Find the value of the derivative (if it exists) at the indicated extremum. (If an answer does not…

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Q: Let R be a plane region with area A whose boundary is a piecewise smooth, simple, closed curve C.…

A: Let's find.

Q: A new fish species is introduced into a lake. Assuming that the population of fish quadruples in the…

A: Solved below

Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

A: As per Bartley guidelines we are supposed to answer only three subparts of one question per post.…

Q: Which of the following is the derivative of x³ + 4x + 1? x² + 4x 3x² + 4 x²+4 3x²+4+1 3x² O

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Q: Find dy. Do not simplify your dx answers cashy (x² + + 7) = x curt y² 1. COS -241

A: As per the instruction, we will be answering only the first question. For (1),…

Q: Find all values of a where the given series converges. Answer: Note: Give your answer in interval…

A: Solution is given below:

Q: area enclosed by enclosed by the Curve Find the X = 2y² and x = 8

A: This question is based on application of integration.

Q: Find curl F and div F given F(x, y, z) = e* siny i+ esinzj+e-² sin x k

A: Given  Fx, y, z = e-x sin y i + e-y sin z j + e-z sin x k We have to find curl F and div F.

Q: Find the length of the curve. 1² (2t+1)³/2 X= 2 3 The length of the curve is 1, y = 0≤t≤2 (Simplify…

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Q: Express the function as the sum of a power series by first using partial fractions. f(x) =  x + 4…

A: Solution: f(x)=x+42x2-5x-3

Q: Prove the identity. sin x 1+ cos x 1- cos x sin x

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Q: Find all solutions to the equation. sec²x + tan x = 1 Write your answer in radians in terms of , and…

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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: How many terms of the series do we need to add in order to find the sum to the indicated accuracy?…

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Q: 6- Write four examples about sketch the graph in polar coordinates from families of cardiod and…

A: Let's find.

Q: = Write the Taylor series for f(x) Find the first five coefficients. Co= C1= C2= C3= C4 e about x =…

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Q: (a) Find the acceleration of the body each time the velocity is zero. Enter your answer as a list if…

A: Follow the procedure given below.

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: 2. Evaluate the following (Express all answer in Rectangular Form): d. √9+ 2i e. 2¹ + ln(2 + i)

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Q: Find the interval of convergence of n²x³n 33n n=1 interval of convergence = (Enter your answer as an…

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Q: Find the arc length L of the graph of r(t). L = r(t) = 11 cos(t)i + 11 sin(t)j + tk, 0≤t≤ 2π

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Q: Find the area between the loops of the limacon r = Area = 5(1 + 2 cos 0).

A: We have to find the area between the loops.

Q: Consider the following. 5 - 10 5 -10 Find an equation for the hyperbola. Find the foci and…

A: Let's find.

Q: Find the exact length of the curve. X = v 3 y (y - 3), 16 ≤ y ≤ 25

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Q: Find the volume of the solid obtained by rotating the region under the graph of the function f(x)…

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Q: Use the graphing guidelines to make a complete graph of f. f(x) = -x³-9x² +1296x-3780

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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: f(x) = ((3x + 7) if x ≤ 4 ax-1 if x > 4

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Q: Consider the following. f(x) = - { $( (²), <1 |x|≥1 Find the x-values at which fis not continuous.…

A: We have to find the points at which the function is the discontinuous.

Q: Find the magnitude of the given vector. (-4, 4, 7)

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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: if x ≤ 2 f(x)= [2x - 5], if 2 3 1. Determine if f is continuous or discontinuous at r = 2 and r =…

A: Solution of the problem as follows