The equation for the conic section with focus (x, y) = (c, 0), direc ricity e 1, by choosing c = de2, has the form: (1-e²)x² + y² + (c²-d²e²) = 0. centricity, coordinates of a focus and equation of a directrix for the co x²y² 9 8 = 1.

Q: I. Find the solution set of the following. 2(1 + cos x) sin x 3. tan X 2 x = [0, π] 1.3

A: Solution 1.3 Given, tanx2= 2(1+cosx)sinx,  x∈[0,π]

Q: Shoppers at Pageturner's Bookstore are tracked, with the following results: 34% visit the…

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Q: PART D: Solving problems involving rational function, equations and inequalities. 1. Suppose you…

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

Q: -3x²+tan(3x-5) Explain the steps you would take to find the derivative of f(x) = (e

A: Our Aim is to find the derivative of f(x)=12e-3x2+tan3x-5 -(i)

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Q: What is the slope of the tangent line to the curve y=−2x^2+8x+2 at the point where x=5?

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Q: Find the equation of the tangent plane to z = ln(x³ + 1) + y³ at the point (0,6,216).

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Q: The area of a rectangle is given by the function A(x) = 3x³ + 6x² + 4x + 8. If the length is defined…

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Q: Find the volume of a solid obtained by rotating the region under the graph of the function x = √y…

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Q: If -2 5 [° f(x)dx = [__ * f(x)dx + [_^¸ ƒ(a)dx − [¯* f(x)dx, -8 what are the bounds of integration…

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Q: Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the…

A: PLEASE LIKE .

Q: Use the rules for sums of powers of integers to compute the sum. 21 Σ; j=5

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Q: Use the graph of y = f(x) for problems 7 and 8. 1010 lim f(x) = 1; HI-4+ lim f(x) = 1; 41144 Use the…

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Q: hat is the average rate of change of f(x) = ln(x+4)/2x+1 over each interval? Give the answer…

A: Given: f(x) = ln(x+4)/2x+1 (a) [-1, 8] (b) 3.45<=x<=5.25

Q: Consider F(x,y,z)=(e³+e²²)₁²+(e¹+z)j + (2xze²²+y)k. Please answer the items below including all…

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Q: For all x ER, it is known that 1. Find the value of f(2022) (0). +∞o 2. Find the exact value of f(x)…

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Q: X √x dx 5-х

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Q: 7. A jar contains black and white marbles. Two marbles are chosen without replacement. The…

A: Solution is given below

Q: Differentiate y = √x + √z 01 O 2√x+1 A+ 2√x + 2√x O 2√x + √x

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Q: The base of the solid is the triangle enclosed by x + y = 11, the x-axis, and the y-axis. The cross…

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Q: Determine the directional derivative of f(x, y, z) = xe³+xsinz+x²y at the point (2,0,4) in the…

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Q: with

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Q: fa¹e² da dx: Applying the integration by parts technique, let Consider the integral Ա 4 X dv = ex x¹…

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Q: Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the…

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Q: 000 Find lim ( -1 Татко 8 41 - 1³ 2-00 1² +41-5 0-00

A: Given, limx→∞4x-x3x2+4x-5

Q: 2. S (4x+5) x²+4x+20 dx

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Q: "풍 2 secx dx tan³x + 4 tanx

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Q: If what does the following integral equal? - 14 73 [6f(x) + 3g(x) - h(x)]dx = - 14 f(x) dx = 11 and…

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Q: On Integration of Rational Fractions. Distinct linear factors Repeated linear factors

A: Given So we do partial fraction to get Distinct linear factor and Repeated liner factor

Q: What is the slope of a line that is perpendicular to y = 3x + 1? -1/3 -3 3 1/3

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Q: 7. Integrate the following indefinite integrals. 3e5x dx 1-2e5x a.

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Q: 3. S (5x-12)dx x3-6x²+8x

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Q: Suppose cot(theta)=-2, t in the second quadrant. Find cos(theta)

A: topic:- trigonometry ratios

Q: what does the following integral equal? L 9(2)dz - [ = ['s g(z)dz = 23 and g(z)dz = 6.5

A: Given:             ∫-9-1gzdz=23              ∫-4-1gzdz=6.5              ∫-1-4gzdz=-∫-4-1gzdz

Q: If what does the following integral equal? 1 d(v)dv= 8 - d(v)dv = 20 and 8 [*d(v)dv = 6.8 7

A: To evaluate the given definite integral.

Q: Differentiate y = (2x³ + 3x² - 1)5 5(6x² +6x)4 30x(x+1)(2x³ + 3x² - 1)4 30x(x + 1)(2x³ + 3x²-1) O…

A: The given function y=2x3+3x2-15 we have to find the derivative of the function

Q: 12. Find the area of the part of the surface z = xy that lies within the cylinder x² + y² = 1. a) I…

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Q: Given f''(x) = 4x + 5 and f'(-1) = 1 and f(− 1) = - 1. Find f'(x) = and find f(4)

A: Let's find function and it's value.

Q: Which of these equations represents a line that is perpendicular to the line in the graph below?

A: Two lines are perpendicular if the product of their slopes is equal to -1

Q: 2 s x² dx x2-4

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Q: Evaluate the definite integral: 0.8 4ze-2%dz = -0.2

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Q: For problems 21 and 22, consider the graph of the function below. Determine the intervals on which…

A: Let's find interval of concave up and down.

Q: 5.f 21 dv (v-1)(v+3)(v-4)

A: We can evaluate the given integral by using the partial fraction method.

Q: 5. Given that f(t) = sint, t=0, t≥π/2 0≤t<π/2 find L{f(t)}.

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Q: 2. Approximate v1.02 +0.02 using an function f(x)=√x + 1 + e*. appropriate local linear…

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Q: Using Part I of the Fundamental Theorem of Calculus, evaluate: d dr 11 t²dt =

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Q: 4. S dy y³-2y²

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Q: The slope of the tangent line to √x+y+√√xy = 2y at the point (2,2) is:

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Q: 2. Find the general / particular solution of the following using variable separable b. mydx = nxdy =…

A: Given: a)  my dx=nx dy       separable equation:        mxdx=nydy integrate on both sides…

Q: For the following exercises, consider a pizzeria that sell pizzas for a revenue of R(x) = ax and…

A: This question can be solved using the concept of maxima and minima.