Homework 3.3 For #1-8, differentiate 1. f(x) = x² cos x

Q: Which of the following statement is TRUE? O A. An ordinary differential equation (ODE) contains…

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Q: Find f'(x) and simplify. f(x) = 8x*(x³ -9) 3 Which of the following shows the correct application of…

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Q: 1. Find the limit. lim X-5 lim x-5 2 √x +11 -6 x-5 2 √√x+11 -6 X-5 =

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Q: 3. Let x² + 4xy + y² = 13. dy • Find dx by using implicit differentiation.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: the difference quotient for the given function. Simplify your answer. Rx)=x²³, f(a+h)-f(a) function…

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Q: dy What is the IF for solving the linear equation: x + = C0SX,x >0 dx 2 O O O O A. B. D. E. MIN 3x 2…

A: To find IF

Q: The degree of homogeneity of the function f(x, y) = (x² - 4y²)-¹/² O A. 1 B.-1 O C. -1/2 D. None of…

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Q: If f(x) = f'(x) = = f'(4) = 3 tan x, then -sin(x) - 3 sec²(x) COS X >

A: we need to find out the derivative for the given function

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Q: ind the limit, if it exists, or type N if it does not ex e√4x²+5y2 lim ,y) →(-2,4)

A: Given query is to find the limit of the expression.

Q: The degree of homogeneity of the function ƒ (x, y) = (x² − 4y²)−¹/² A. 1 B.-1 C. -1/2 D. None of the…

A: The given function is fx,y=x2-4y2-12 We have to find the degree of the homogeneity.

Q: Eliminate the arbitrary constants of y=c₁e*+cx*— sin3x

A: We use differentiation to Eliminate the arbitrary constant, we differentiate the given equation as…

Q: Give the implicit solution of y'my-x³-2 Oe-2x = y²(x²+c) Oe²-y²-c 2x Oe² = x²(x²-c) 0²¹-y²(x²-c)

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Q: Use the Law of Cosines to determine the indicated angle 8. (Assume a = 126.5, b = 59.5, and c = 159.…

A: Given, a=126.5, b=59.5 and c=159 Aim: Find θ

Q: -3 Σ Σ 4 Τ 1 Σ k=i (k + 2)(k + 3) IME 1 4*+2 7K-1

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: f(x): '(x) = *'(3) = 4 sin x 1 + cos x 4 1 + cos(x) then B Or

A: Given query is to find the derivative.

Q: Let z=xy/(5x^2+4y^2). Then:     ∂z/∂x =     ∂z/∂y =

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Q: find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P.…

A: Given, y=1x,  Point P-2, -12

Q: Solve for the IF of the equation y(x + y + 1)dx + x(x + 3y + 2)dy = 0 OA. O B. OC. ev eLny HA O D.y…

A: given    y(x+y+1)dx+x(x+3y+2)dy=0   it is of the form Mdx+Ndy=0   where M=y(x+y+1),    and…

Q: f(x) = x5 + 8

A: Given, fx=x5+8

Q: Which of the following is a non-homogeneous function? tan³y/x | xLnx − xLny x³ - xy + y2 (y² +…

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Q: present

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Q: Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal…

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Q: Eliminate the arbitrary constants of y=ce*+₂4-sin3x

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Q: Find the middle term in the expansion of:

A: Gievn expression:- 3x+x310

Q: Determine all the methods that can be used to solve the differential equation ( 3x ²y ³ — 4x − y ³)…

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Q: If y=f(x)=7e^x + 3x^4 - 20x - 5 , Find the x-intercept of the tangent line at x = 0 to the graph of…

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

Q: 1. Given that lim f(x) = −1 and lim g(x) = 8, find the following limits. x-3 (a) lim (2g(x)-4f(x))…

A: This question can be solved using the concept of limits.

Q: Solve for the IF of the equation y(x + y + 1)dx + x(x + 3y + 2)dy = 0 OA. O B. ey O eLny °A O D.Y O…

A: given    y(x+y+1)dx+x(x+3y+2)=0

Q: Solve for the value of constant C in the equation: (2x + 3)y' = y + (2x + 3)¹/2 when x = -1 and y =…

A: To solve for the value of constant C in  the equation: 2x+3y'=y+2x+312when x=-1, and y=0.

Q: t is the object's velocity when t=6? far has the object traveled in 6 hours? n is the object…

A: Topic:- application of derivatives and algebra

Q: Suppose f (x, y, z)= + P = (2, 4, 3). A. Find the gradient of f.

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Q: (5) Find the center of mass of the region bounded by y = sin x between x = 0 and x = 7 above the…

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Q: K A rain gutter is to be made of aluminum sheets that are 12 inches wide by turning up the edges…

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Q: What is a suitable integrating factor that can be used to solve the equation dy dx O A. O B. 3 ex…

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Q: Find all values of n such that y = x" satisfies x²y" - 20y = 0

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Q: ating factor (IF) of the equation: - 4x²y + 2xy² + xy + 2y)dx + (2y³ + 2x²y + 2x)dy = 0 e of the…

A: We will find upon multipication which factor make above differential equation exact .

Q: Obtain the differential equation whose general solution is y = C₁ + c₂e³x О А. y" - 3y' = 0 OB. 3y"…

A: the given  general solution  y=c1+c2e3x⇒y=c1e0(x)+c2e3x

Q: Use the graph of f to determine each of the following. Where applicable, use interval notation. a.…

A: The domain is the set of all possible input x values while the range is the set of all possible…

Q: the space curve (t) = (2t, t², 2t)

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Q: (g) Differentiate g(x) = V/1-2²-cos¹ (√2) COS (h) Find (1) Find do [sec (arctan (62))] de sin-¹(cos…

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Q: Solve for the value of C in the equation: O A. 1 OB. 2 O C.3 O D. 4 E. None of the Choices dy dx…

A: Find integrating factor of linear differential equation

Q: Which of the following equations OA. (2x sin y + y)dx + (x² cos y + x)dy = 0 OB. 1 dx-dy-0 y O E.…

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Q: 11 11 Given "f(x)dx = 34 and g(x)dx = -5, find the following: ₁₁ [4f(x)-3g(x)]dx 11 O -151 O 151 O…

A: We have, ∫-411fxdx = 34∫-411gxdx = -5 To evaluate: The value of ∫11-44fx-3gxdx.

Q: The partial fraction decomposition of f(x) X - 5 + g(x) x + 5' where 56 x² - 25 can be written in…

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Q: Solve the following D.E. using two(2) methods (y-2) dx (x - 4y + 5) dy

A: We have to find the solution of the given differential equation.

Q: fies a(t) = −9.8 + mv(t)², where v(t) is velocity, negative since the object is falling, and k is a…

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Q: Which of the following equations is NOT an exact equation?

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Q: Find all points where the function is discontinuous. OA. x=0 OB. x= -2, x=0, x=2 OC. x= -2, x=2 OD.…

A: Given query is to find the points wherw function is discontinuous.

Q: Sketch the region bounded by the curve x 2 = y and the line x = volume of the solid generated by…

A: solution:-the region bounded by y=x2-2 & x=y+2revolving around y=1