PROBLEM: Find the differential equation of the family of hyperbola with center and transverse axis on the y-axis (the center is not the origin). Let the y-coordinate of the center be fixed. HINT: The center is either in the positive or negative y.

Q: 2) Consider the function f(x) = x + sin x defined only for x € [1,4]. Fill in each blank with a…

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Q: Find the directional derivative of the function f(x, y, z) = √xyz at the point (3, 2, 6) in the…

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Q: Use polar coordinates to find the volume of the given solid. V = Inside the sphere x² + y2 + z² = 25…

A: Given sphere x2+y2+z2=25 And cylinder x2+y2=1

Q: FIND F'(x) for F(x) = -7 w/out USING the √5x³-20x quotient TULE

A: Given query is to find the derivative of the function.

Q: x=t+3 and y=²+2t Part: 0/2 Part 1 of 2 (a) Eliminate the parameter and write an equation in…

A: The parametric equations are x = t+3                         .........1y = t2+2t…

Q: If  f(x) = 4x2 − x3,  find  f ′(x),   f ″(x),   f ‴(x),  and  f (4)(x)

A: Topic- derivative of a function We are given, f(x) = 4x2 − x3 and we know thatddxxn=nxn-1

Q: Use the formula for nCr to evaluate the expression 4C4.

A: Given: The given expression is:  4C4. n = 4 r = 4 Formula Used: Crn = n!r!(n-r)!

Q: 2) The total cost in dollars of producing x lawn mowers is given by C(x) = 4,000+ 90x- -. Find the…

A: Given query is to find marginal average cost.

Q: Use the Fundamental Counting Principle to solve:A restaurant offers the following lunch menu. Main…

A: Given data:- A restaurant offers the following lunch menu:- Main Course      Vegetables…

Q: 2y Suppose f(x, y) = sin X in the direction of (1, 2). Then, 2y 2y i (a) ▼ f(x, y) = cos(2)21 +21) X…

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Q: Does the parabola y=2x^2 -13x + 8 have a tangent whose slope is -1? If so, find an equation for the…

A: Topic- Slope of tangent and equation of a line We are given an equation of the parabola y=2x2-13x+8…

Q: lim asin x→0 | cr x

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Q: A farmer is building a fence to enclose a rectangular area against an existing wall, shown in the…

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Q: cample: y = √sin(x4 - 6x) find 11-Sin(x

A: Given function:- y=sinx4-6x

Q: Evaluate the limit If the limit does not exist enter DNE. Limit Number = lim x 6 x2 x-6 6 x

A: To evaluate the following limit.If the limit does not exist then to enter DNE.limx→6 x-6x2-6x

Q: Given the matrix find A. Write A as input your answer below: a1 = 012 021= 022= H EI I EE A³ - [:…

A: The matrix is given by A = 220-3 To evaluate: The value of A3

Q: Find the derivative of: – 7 sin² ( – 8x³). Hint: sin²(x) = [sin(x)]²...so use the chain rule…

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Q: Given lim f(x) = -5 and lim g(x) = -12, evaluate lim [5f(x)-2g(x)]. X→ 11 X-11 X→ 11 O lim…

A: Given that: limx→11f(x)=-5, limx→11g(x)=-12

Q: For the piecewise linear function, find the following. (If an answer does not exist, enter DNE.)…

A: NOTE: Refresh your page if you can't see any equations. . the given piece-wise function is

Q: Find the directional derivative off at P in the direction of a. ƒ(x, y) = 5x²y³; P(2, 2); a = 3 i −…

A: This question can be solved using the concept of partial derivatives and vectors.

Q: Use the Fundamental Counting Principle to solve:How many different four-letter radio station call…

A: Fundamental counting principle:- A rule for counting all possible outcomes in a scenario is known as…

Q: If lim x approaches 1 ƒ(x) = 5, must ƒ be defined at x = 1? If it is, must ƒ(1) = 5? Can we conclude…

A: Given that If x→1 f(x)=5limit approaches 1 f(x)=5, must f be defined at x=1? If it is, must f1=5 .

Q: Question-Solution-Final Answer-Conclusion format) - Generate solution of the first-order…

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Q: Evaluate where f(x) = 7 x + 8. If the limit does not exist enter DNE. Limit= Number lim h→0 ƒ(1+h) —…

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Q: Find parametric equations representing the line segment joining P(-3, 2) to Q(2, -1) as (x(t),…

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Q: Consider the ellipsoid x² + y² + 4z² = 41. The implicit form of the tangent plane to this ellipsoid…

A: Please see the below picture for detailed solution.

Q: Find the arc length of 2 + 3/2 from x = 1to x = 4.

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Q: 4. Consider the initial value problem y = x+y, y(0) = 1. (a) Use Euler's method with h = 0.1 to…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Use algebra to rewrite the expression BEFORE you differentiate. 8x¹7 - 2x¹4 14 x11 A) 32x³ - 2x D)…

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Q: dy For items 13-14, consider the function y=√ 6x-2 whose derivative is given by dx 3₁√/6x-2 2(3x -…

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Q: 11 Find the derivative of f(x) = -15sinx + +3√√x-5. X

A: Given function:- fx=-15sinx+11x4+3x7-5

Q: 6 5 4 3 نا 2 1 ¦ y = f(x) 01 2 3 Enter each answer as a whole number or a fraction, or DNE for Does…

A: The graph of the function is To evaluate: The values of limx→3+fx-4fx+4, limx→3-ffx+4 and…

Q: Find the derivative of the function r = sin(0³) cos(30). dr do

A: Solution

Q: Find an equation for the plane that passes through the following points. (3, −1, 5), (0, 0, 6), and…

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Q: lim X->15 x+10 5 x-15 c/+X

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Q: d (h) Find sec (arctan (0~))] do

A: We need to find out the derivative.

Q: find f + g, f - g, f # g, and fgfor each pair of functions. State the domain of each of these…

A: Given, fx=3x2+x+1gx=3x

Q: Use Lagrange multipliers to find a vector in 3-space whose length is 6√3 and whose components have…

A: Let vecter to be xi+yj+zk Then length of vector = √(x^2+y^2+z^2)=6√3

Q: (e) Write out the first five terms of the sequence, determine whether the sequence converges, and if…

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Q: Set f(x) = 1 7x³ + 3x + 2 . (1, 1/12) is on the graph of ƒ. Find (ƒ-²¹) (¹2). The point 1,

A: The solution to find the value of inverse of f(x) at 1/12 is as follow.

Q: Find an equation for the plane containing the two (parallel) lines v1 = (0, 1, −3) + t(8, 2, −1) and…

A: Find an equation for the plane containing the two (parallel) lines  v1 = (0, 1, −3) + t(8, 2, −1)…

Q: campus of 5000 students, one student returns from vacation with a contagious and long-lasting flu…

A: Here we have The total number of students infected after t days. y=5000  (1 + 4999e-0.8t)…

Q: 3. Given the vector equation r(t) = (3+4 sint, -2 + 4 cos t), 0 < t < 2n, you should recognize that…

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Q: A coroner arrives at a murder scene at 7 p.m. She finds the temperature of the body to be 84 3°F.…

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Q: eliminate  the arbitrary constant a and b: y= a+be^x

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Q: Geometry A wire of length x is bent into the shape of asquare.(a) Express the perimeter p of the…

A: Given: A wire of length x is bent into the shape of a square. (a) To express the perimeter p of the…

Q: A farmer is building a fence to enclose a rectangular area consisting of two separate regions. The…

A: Find the dimensions of the region which enclose the maximum area

Q: 5) Square PQRS with side length x is subdivided into four triangular regions as shown such that area…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: A triangle has vertices (0, 0, 0), (1, 1, 1), and (0, −8, 9). Find its area.

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Q: On the day of a child’s birth, a deposit of $P is made in a trust fund that pays 8.75% interest,…

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