x=t+3 and y=²+2t Part: 0/2 Part 1 of 2 (a) Eliminate the parameter and write an equation in rectangular coordinates. The equation in rectangular coordinates is y ww

Q: ch of the described curves, decide the an equation for the curve. (a) A line through the origin that…

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Q: Obtain the differential equation whose general solution is y = C₁ + c₂e³x. A. B. E. y" - 3y' = 0…

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Q: Solve for the value of C in the equation: dy − (y + xy5)dx = 0 when y(0) = 1

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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: SIT lim t-0 CATA 3+t-√3-t t anot

A: To find the limit.

Q: Determine the solution of the differential equation: dx dy y 4² + X y

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Q: (a) Using a graphing utility, graph f1x2 = x3 - 9x for- 4 ... x ... 4.(b) Find the x-intercepts of…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Evaluate the following limits, making sure to justify your calculations as much as possible: lim…

A: See this solution in below.

Q: If the endpoints of a diameter of a circle are 14, - 52 and 1 - 6, 32, find the center and radius of…

A: Given: The endpoints of a diameter of a circle are (4,-5) and (-6,3). To find: The center and radius…

Q: Compute f' and find an equation of the tangent line to the graph at x = a. f(x) = 9x-³, a = 5. (Use…

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Q: 1. Separation of variables/ a. xy³ dx + (y + 1)e-*dy = 0

A: Here we have to solve the given differential equation

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: Use the formula for nCr to evaluate the expression 7C7.

A: Given: The given expression: 7C7. Formula Used: Crn = n!r!(n-1)!

Q: Which of the following equations can be made into a linear differential equation? A. (x² + xy)dy -…

A: To check: Which of the given differential equations is linear?

Q: Evaluate the following integral, showing all calculus and algebra work. 2x² √2x²+x=1d + x - 1 -dx

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Q: Evaluate the following integrals: 8 3 S(4 + 3√x) (2x + √x ³) "dx

A: SOLUTION-

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

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Q: The answer was not correct... i think they were wanting some kind of answer closer to like…

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Q: Find the value of the constant b that makes the following function continuous on R. 8x - 26 f(x) =…

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Q: Find the slope of the line containing the points (3, - 2) and (1, 6).

A: Given data:- The given points of line is, 3, -2 and 1, 6

Q: If f(x) f'(x)= -3x sin²(x) + 3x cos² (x) + 3 cos(x) sin(x) = 3x sin x cos x, find Find f'(4) =

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Q: Question 2 Solve for the value of C in the equation: dy − (y + xy5)dx = 0 when y(0) = 1 A. 1/4 B.…

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Q: Question 16 Eliminate the arbitrary constants of y=c₁e³+₂x4-sin 3x

A: We are given a differential equation,  y = c1ex +c2x4 -sin3x   ... @ We havet o eliminate arbitrary…

Q: compute the acute angle formed by the asymptotes of the hyperbola x^2-3y^2-8x=14

A: Explanation of the answer is as follows

Q: Find the area between the curves (Hint: Your answer will be in terms of a.) The area is f(x)=x and…

A: area is=a3/6

Q: A mathematical model for the average of a group of people learning to type is given by N(1) (2 hours…

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Q: 9. For what value of a is the following function continuous at every x? a x+6a, x22 8, x<2 Select…

A: Given query is to find the value of "a" that makes function continuous everywhere.

Q: Which of the following equations can be made into a linear differential equation? OA. (x² + xy)dy -…

A: Option D

Q: Geometry A semicircle of radius r is inscribed in a rectangleso that the diameter of the semicircle…

A: Area of the rectangle=length×breadthPerimeter of the rectangle=2(length+breadth)given :-Radius of…

Q: Give the implicit solution of y'=y=xy²e Oe-2x = y²(x²+c) O e ²x = y²-c O e²x = x²(y²-c) е…

A: We will find the required  solution of given differential equation.

Q: A B C D lim /(x) = 0 x+2+ lim f(x) = 2 x →-2+ lim /(x) = 0 x+2- lim f(x) = -3 x--2 -5-4-3-2-1 Y -3-…

A: Find limit of function

Q: 7) Find the horizontal asymptote, if any, of the given function. 2x³-3x-9 f(x) 9x³-5x +3 A)y=5 8) If…

A: Here we have to use the concept of limits

Q: 5₁ 4 2 7777 Find Find 7/2 Q The graph of the function f(x) = sec x is given above for the interval x…

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Q: Find the explicit solution of dy/dx=2xy² + 3x²y², y ( 1) = − 1 O 1/y=3-x²-x3 Oy=x²/2+x²³/3-3…

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Q: Use the geometrical series formula to evaluate the following: k=2 3 5k

A: Given :- ∑k=2∞35k

Q: 2. Find the 2nd derivative of sin (x²-1) y *2cos(x^2-1) 4x^2 tan(x^2-1) 2cos(x^2-1) + 4x^2…

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Q: Sketch the region bounded by the curve x² - 2 = y and the line x = y + 2 and find the volume of the…

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Q: If the slope m of the graph of a linear function is ,the function is increasing over its domain.

A: If the slope m of the graph of a linear function is _______, the function is increasing over its…

Q: A car sharing service offers a membership plan with a $30 per month fee that includes 10 hours and…

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Q: Find the exact length of the curve. y=ex, 0≤x≤ 3

A: Length of curve =∫ab1+dydx2dx

Q: Solve for the value of C in the equation: A. 1 B. 2 C. 3 D.-1 (2xy4e³ + 2xy³ + y)dx + (x²yªe¥ − x²y²…

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Q: Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.…

A: degree=3

Q: Find the volume of the solid bounded by the planes x = 0, y = 0, z = 0 and the plane 3x +2y + z = 6.

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Q: lim asin x→0 | cr x

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Q: 2. 8[][

A: The objective of the question is checking the convergence or divergence of the given series.

Q: Evaluate using integration by parts or substitution. Check by differentiating. (2x²-7x) e7x dx √(2x²…

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Q: D. Verify the general solution and obtain the particular solution using the given initial…

A: Differential equation

Q: f(x)= (ln x)^3 f'(x)=

A: Given, f(x)= (ln x)^3

Q: If f1x2 = x2 - 4, find f1 - 22.

A: Given, fx=x2-4

Q: Find the general form of f if f'(x) = 5f(x).

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