A. Find the derivative of the following functions. Whenever possible, express answer in factored form 4. y

Q: For the curve 2² - 4xy² = y³ +9, do the following:

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Q: Find y" by implicit differentiation. 4x³ + 3y³ Зу3 = 4

A: Quotient Rule of differentiation : ddx(uv) =v.dudx-u.dvdxv2.

Q: Graph and find the vertical asymptote of the function: x² +1 3x-2x² y =

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Q: tion 8 of 22 Calculate the first, second, and third derivatives of y(x) = x² e²x (Use symbolic…

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Q: Find the partial fraction decomposition of -6x - 16 x² + 6x + 8

A: -6x-16x2+6x+8

Q: The graph of a derivative f' is shown to the right. Use the information in the graph to determine…

A: Given that the graph of a derivative f' is shown to the right.

Q: 5c

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Q: If income is continuously collected at a rate of f(t) dollars per year and will be invested at a…

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Q: 6) Given x²-4y²-16z² = 4 (a) Rewrite into standard form and name/identify the type of surface. (b)…

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Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of…

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Q: 2. Prove that the general solution to ndm + mdn + mn (3dn + dm) = 0 -3n-m is Cmn = e

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Q: Find g'(3) given that f(3) = -2 and f'(3) = 4. a. g(x) = 3x² – 5ƒ(x) 2x + 1 b. g(x) f(x) . . e

A: Solution is done in steps

Q: 1. Given f(x, y) = x³y − 3xy + y² – 1. (a) Find the critical points of f. (b) Use the Second…

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Q: 3x²+2x²+x iii) fi dx

A: I am attaching image so that you understand each and every step.

Q: If f(x) ƒ'(x) = f'(5) = = tan x sec x 2

A: Topic- Derivative of a function  Note: As per bartleby guidelines, we are supposed to answer only…

Q: A B Which of the following is not a first order linear differential equation? dp dt dy-y²-y +2Pt = P…

A: Explanation of the answer is as follows

Q: 5. Consider the polar curves having the equations r = 3 sin 0 and r = 1 + sin 0. a. Sketch the…

A: Given curves are r= 3 sin(theta),r=1+sin(theta)

Q: Use the graph of the function to find its domain and range. Write the domain and range in interval…

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Q: (e) Find equations of the horizontal and vertical asymptotes of the graph of f(x). HA VA:

A: Given query is to find vertical and horizontal asymptotes.

Q: Given the following functions, find and simplify (f.g) (5.5). Provide your answer below: (f.g)(5.5)…

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Q: Evaluate with the Simpsons rul

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Q: Suppose the demand for a certain brand of a product is given by D(p) = 352 find the demand function…

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Q: Calculate the third derivative of y(x) = (4x² + 2) (5x³+3) (Use symbolic notation and fractions…

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Q: Find the equation of the plane which makes intercept 2,3 and 4 on the co-ordinate axes

A: Given data, a=2 b=3 c=4

Q: Problem 8. (a) Je* sin (2) (b) ) [(x +3 (c) [²² +3) In (x) dx (In (x))² dx Calculate each of the…

A: As per the guidelines I am supposed to do the first question among multiple questions. So here I am…

Q: 1. A particle moves horizontally according to the law s = t³-t²- 24t + 1. (a) Where is the particle…

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Q: Is the statement below true or false?   The differential equation f(x)dx + g(y)dy = 0 is exact.

A: The statement is false.A differential equation Mdx+Ndy=0 is exact if and only if ∂M∂y=∂N∂x. see…

Q: elnx 8) fex dx g) √1-e²t dt (Hint: let u = e¹) h) fx dx dx (let u = x¹/2)

A: g)∫elnxxdx

Q: 3. A 13-foot ladder is leaning against a house when its base starts to slide away. By the time the…

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Q: Find the derivative: Y = y' - 10 sin(x) + 3 5x9 - 2 =

A: The given function is y=-10sinx+35x9-2 We have to find the derivative of the function

Q: Let _ƒ'(x) = f(x) = (–9x² − 7)³(-9x² + 2)-¹2 -

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Q: Evaluate OI 4 sin ³x dx sin*x + C -sin¹x + C +cos³x + C -cost + +C cost --cos³x + C

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Q: The graphs of f and g are given. Use them to evaluate each limit, if it exists. If the limit does…

A: As per our guidelines we are suppose to solve only three sub-parts of a question. Kindly re-post the…

Q: Evaluate the following integral by interpreting it in 3 1₁ (2 - x) dx =

A: Graph of  | x | graph of - | x | is reflection of | x | about x axis  graph of 2 - | x | is…

Q: Solve (1- + xp z_(hx [y² + x² (1 1)-2] dy : dy = 0 xy)

A: We have to solve the given differential equation.

Q: Find derivative of the function (5t^2 / 3t^2 +2)^3 using the chain rule.

A: The function is given by y = 5t23t2+23 To determine: The expression of the first derivative of the…

Q: #4 #5 3 L (5+ JO (5+3 cos x) dx 3 [x²² O x² ex dx

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Q: Horizontal asymptote(s): y = f(x) = Find the horizontal and vertical asymptotes of f(x). If there…

A: We need to find asymptote.

Q: 2) Is the discontinuity x = 0 for the function f removeable or non removeable. Fully justify your…

A: We need to explain removable or non removable continuity at x=0.

Q: ider the following. f(x) = 1 x+2 (a) State the domain of the function. all real numbers x all real…

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

Q: Graph the functions on the interval [-7,7]. Include all asymptotes and labels on your graphs where…

A: We have to plot the graph of 1) y= sin x 2) y = cos x 3) y= tan x Under the given interval with…

Q: Instructions: Given: y=-3(x-1)² +12 Match column A: Match the correct answer from column B with each…

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Q: x-1, if x ≤-2 f(x)=2x-1, if -2 4

A: Use bigger dots for equality

Q: x² dx + xy = 1 2 dy dx 3) X (linear equation)

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Q: Solve the inexact differential equation ydx + (2xy-e-2y) dy = 0.

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Q: 1. U Substitution (a) These integrals may require one or more substitutions. i. [√x - x√xdx ii. S/²…

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Q: 1. Center at (-3, 9), a vertex at (-6, 9), and conjugate axis of length 8.

A: As per Bartleby guidelines we only give first question answers. Please repost for other parts.

Q: The integrating factor r"y is multiplied to the differential equa- (2y 6x) dx + (3x - 4x²y-¹) dy = 0…

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Q: 1. Sketch a graph of a function that has the features to match the following: i. It has x intercepts…

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Q: X lim x→0 √1 + 8x − 1 - ||

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