. Find the equations of the tangent line and the normal line to the curve 3r O at the point (0 A

Q: Find the derivative of the function. y' = y = 9 tan-¹(x - -1(x - √ ₁ + x²) 9 1+x² 18x 3 (1 + x² ) (…

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Q: Write the first five terms of the sequence: [11 Inn n a₁ = Determine whether the sequence converges,…

A: To find the first five terms of the given sequence and to determine whether it diverges or not.

Q: Given that calculate the following partial derivatives af 3x af ду = 22 f 0x2 02 f ду2 22 f ?хду 02…

A: Since you have asked a question with multiple parts in a single request we would be answering only…

Q: Find the 12th-degree Taylor polynomial for f(x)=e^(2x^3 ) centered at 0.

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Q: The so-called "shark fin" piecewise function consists of two quadratic polynomials: x² +1 on [0, 1]…

A: If a point (c,d) lies on the curve y=f(x) then it satisfies the equation of the cutve⇒At x=c,y=d…

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A: Solution is given below:

Q: Suppose that f(x, y) = xy. The directional derivative of f(x, y) in the directional (2, -6) and at…

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Q: If 4x − 2x² <f(x) <x² - 2x +3 for - all real numbers except for x=1, then

A: We have to solve given Questions.

Q: The manager of a large apartment complex knows from experience that 120 units will be occupied if…

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Q: Find the equation of the specified line. y(x) = through (-4, 8) with slope -1

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Q: 3x The equation r(t) = (3 cos t)i + (5 sin t) j+(3t) k is the position of a particle in space at…

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Q: Algebraically determine the following limits for the piecewise function defined as: y = [(x+1)²-2_x1…

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Q: Nonrepeated Linear Factors In Exercises 9-16, express the integrand as a sum of partial fractions…

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Q: Assume A = A₁ + A₂ and A, B = 0. If A₂ = kB, show that k = ● (5) (6) Use the formula x = r' (t)…

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Q: Question 2 Classify each differential equations as separable, linear, homogeneous or Bernoulli…

A: Given differential equation dydx = 7y-x

Q: 4. 5. Dx cotx -sin csc x-1 csc x+2

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Q: What is the exact value of the expression? tan (7) + sin (57) · cos (− ³) 4√3+3√6 12 O O 4√3+3√2 12…

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Q: If f and g are the functions whose graphs are shown, let u(x) = f(x)g(x) and v(x) = f(x)/g(x). ya 0…

A: Given :

Q: Find the values of x, y and z that correspond to the critical point of the function f(x, y) = 3x² +…

A: The given function is: fx,y=3x2+4x+6y+4y2 To find the value of x, y, z that correspond to the…

Q: Find the direction at the origin of the curve, (a²-b¹) y=x (x-— a)¹ — bªx. Ans. 45° with OX. What…

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Q: The sum of the perimeters of an equilateral triangle and a square is 19. Find the dimensions of the…

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Q: 3. Sketch a graph of a function, f(x) with the following 4 characteristics (thinking) i. lim f(x) ‡…

A: To graph the function with the given characteristics ,first we write a function by using the…

Q: Can you show me the steps how to simplified this equation. I am having trouble with the square…

A:

Q: the exact x-coordinate where there is a horizontal tangent line to the graph of f(x) = x8ª. In(x)…

A: We will find the required.

Q: Answer the ff. differential equations. Show complete solutions. 1.) (r+sin-cos)dr +r(sin 0 + cos0)d0…

A: Topic: Differential Equation   The answer is given below:

Q: Examine whether equality of cardinalities is an equivalence relation on sets: i.e. if it is…

A: We have to show equation of cardinaties is an equivalence relation on sets.

Q: For q units of a product, a manufacturer's cost is C (q) dollars and revenue is R(q) dollars, with C…

A:

Q: 2.] xydx + (x² + y² + y )dy = 0 y(0) = 1

A: To solve the following initial value problem. xy dx+x2+y2+y dy=0, y0=1

Q: 20 Write the equation of the _3x² + 5y² + 2xy = 76 tangent at the point (-2,42. line to

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Q: Evaluate the integral. log 4(x + 2) x+2 2 0 0 log 4(x + 2) x + 2 dx = dx

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Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 2x sin(xy)…

A: We will find the required.

Q: Given that f(x) = x³h(x) h(-1)=5 h'(-1) = 8 Calculate f'(-1). -33 Hint: Use the product rule and the…

A: Formula used ddxxn = nxn-1ddx( u.v ) = udvdx + vdudxGiven f( x ) = x5h( x )

Q: Find the derivative of the function using the definition of derivative. g(x) = = √9+ 2x g'(x) =…

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Q: A family purchased a home for $125 000. Appreciation of the home’s value, in dollars, can be…

A: Instantaneous rate of change at the start of the eighth year.   Instantaneous rate of change is the…

Q: Which of the following is an ordinary, linear differential equation of order 2? +k²xt = 0 d²x +k²x =…

A: Find which equation is linear differential equation of order 2.

Q: Find the derivative of the function. h'(x) = h(x) = √ 1 -X 2 1-x² √1-x² sin-¹(x) X

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Q: Show that the function f(x, y) = points where it is defined. arctan(y/x) is harmonic, at all those

A: Introduction: A function u(x, y) is known as harmonic function when it is twice continuously…

Q: Use the Special Integration Formulas (Theorem 8.2) to find the indefinite integral. (Use C for the…

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Q: (4xy + 3y² − x) dx + x(x + 2y)dy = 0

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Q: s) Given the acceleration, initial velocity, and initial position of a body moving along a…

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Q: lim X18 2x³ - 3x x³+4x²

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Q: Set up the definite integral required to find the area of the region between the graph of y = 16 -…

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Q: f(x)= 2x^3 + 12x^2 -270x The derivative of this function can be shown to equal f'(x)= 6x^2 +24x…

A: Given function f(x)=2x3+12x2-270x As per our  guidelines we are supposed to answer only  three…

Q: Use the graph below to estimate the marginal cost at the following levels of production. Round your…

A: To Find: Marginal cost when the quantity is: (i) 18,000 (ii) 14,000

Q: Carbon-14 has a half-life of 5730 years. A fossil is 10,000 years old. What percent of carbon-14…

A:

Q: 1. Find the particular solution: y" + 3y + 2y = te-2. 2. Find the particular solution: y" - 2y + 2y…

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Q: Evaluate the integral. 8 dt 64 + t² 6

A: D=∫08dt64+t21+tan2x=sec2xd dx(tanx)=sec2x

Q: Roll a fair die and let x be the square of the score that shows up. Write the probablity…

A: This is a problem related to probability distribution. Please follow the procedure given below.

Q: Evaluate the definite integral. 1 6². lo (8v + 1)² 2 dv

A: Given: ∫011(8v+1)2dv

Q: Two friends Korin and Lorie are running a marathon along a straight road. Assume that their…

A: