1. Sketch the graphs of x = 6y-y² and x = y² - 8. Shade the region bounded between the two curves. Hence, find the area of the region shaded.

Q: Solve the differential equation by variation of parameters. y" + 2y' + y = et In(t) y(t) =

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Q: Khalil's Babysitting Earnings Khalil charges a constant hourly rate. When he babysits What does the…

A: We have to find the function that represents the amount.

Q: Use implicit differentiation to find dz/dx and dz/dy. X - z = arctan(yz) 218 дх 3: ду = = 1 22 yz +1…

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Q: Determine whether the integral is convergent or divergent. x² V6+x³ [ convergent Ⓒ divergent If it…

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Q: This question has several parts that must be completed sequentially. If you skip a part of the…

A: We need to fill in the blanks.

Q: Calculate given the following functions. O a. O b. O C. дz Əv O d. дz ὃν дz əv дz Əv дz Əv || Z = 2x…

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Q: Solve the differential equation by variation of parameters. y" + 2y' + y = e-t In(t) y(t) =

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Q: Three different forces act on an object. They are: F₁ (8,5) (1,7) F₂ F3 (0, 3) = - = Find the net…

A: The three forces are given as: F1→=8,-5 F2→=1,7 F3→=0,3

Q: Find the derivative of f (x) = 30 6/2x+1

A: Given problem:- f(x)=-302x+16  TO Find:- Deriative of f(x)

Q: Evaluate the function at the given value of the Independent variable. Simplify the results. (If an…

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Q: Find the average value have of the function h on the given interval. h(u) = (In(u))/u, [1, 6] have =…

A: The function is given as , hu=lnuu find the average value have on 1,6.

Q: Find y" of y=- y" = y" = O y" = y" = X-1 2 (x-1)² 2 (x - 1)³ 1 (x - 1)³ -2 (x - 1)³

A: Topic = Derivative

Q: Question 18 -6 -5 -4 -3 -2 -1 8+ (2) 7 65 4 32 My 1 -1 -2 -3 --4- ✓ to t 1 3 Find an equation for…

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Q: 5. The sum of thrice a number and two equals 6 less than four times the number. Find the number.

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Q: 000 is budgeted for production of the product, determine how that amo ion will be maximized when…

A: We are asked to find the maximize the profit

Q: The count in a bacteria culture was 300 after 15 minutes and 1500 after 40 minu count grows…

A: We will solve.

Q: Given differential equation y""-ay" -4y' + 8y = e²-³x +8x⁹ (D³ - 20² - Auxilary equation 2 4D +8)y=e…

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Q: Evaluate the iterated integral by converting to polar coordinates. -x² IT (x² + y²) dy dx dr de-

A: We can evaluate the given iterated integral.

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

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Q: Why is the Second Derivative Test inconclusive when f"(c) = 0? Explain. Please use clear…

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

Q: Let f be the piecewise function i. 11. f(x) = (x³ + 6x² + 8x x + 2 x 1 Sketch the graph of f. Based…

A: Solution is given below:

Q: Solve the following inequality. (x+5)(x+3)(x-7) <0

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Q: Ow Find using the appropriate Chain Rule for w=y³-5x²y where x = es and y = e, and evaluate the…

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Q: The population of mosquitoes in a certain area increases at a rate proportional to the current…

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Q: The given family of functions is the general solution of the differential equation on the indicated…

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Q: Set up integrals for both orders of integration. Use the more convenient order to evaluate the…

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Q: Determine whether the vector field is conservative. F(x, y) = 6y6(yi + 7xj) conservative not…

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Q: 16-1

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Q: Examine the function for relative extrema. f(x, y) = 2x² + 7y² - 4x − 14y + 12 (x, y, z) = ((No…

A: Given function: fx, y=2x2+7y2-4x-14y+12

Q: N g'(x) = Find the derivative of the function g(x) = (3x²5x + 1)e²

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Q: Find the indefinite integral by making a change of variables. 1 √ 4 + ²√2x² dx

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Q: 4. (x-1)(2x³+2x²+3x+2) dx x³ (x+1) r 5. csc ³0 de

A: We have to integrate question no 4 and 5.

Q: A force of 720 newtons stretches a spring 4 meters. A mass of 45 kilograms is attached to the end of…

A: This is a problem related to differential equation. Please follow the procedure given below.

Q: Step To sketch the graph of f(x) = 4x - x², first construct a table of values by evaluating the…

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Q: Solve the given differential equation by undetermined coefficients. y" - 2y' - 3y = 4ex - 6 y(x) = 4

A: See this solution in below

Q: Exercise (b) Find the slope of each secant line. Step 1 Recall that the slope of a non-vertical line…

A: Since the secant line is passing through another point Q(3,3) Therefore we will substitute x = 3 in…

Q: Solve the given differential equation by undetermined coefficients. y" - 2y' 3y = 12ex - 12 y(x) =

A: See  the details solution in below

Q: Evaluate the triple iterated integral. LLL Jo π/4 6 6-r rz dz dr de

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Q: A) Let g(x)=x² (5x+24 (2x + 8 a) lim x-1 b) lim X-0 a) lim g(x), lim g(x) x--3 x-0 B) Find the…

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Q: Jse polar coordinates to describe the region shown. y -2 -1 1 1 2 Xx

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Q: need

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Q: Let - fot² Find the average value of f on the interval [0, 1]. f(x) = dt.

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Q: (-tanx) ydx + Inlexy cos x| dy = 0

A: We need to find out the general solution of the given differential equation.

Q: g'(x) = Find the derivative of the function g(x) = e² 52+3

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Q: Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary Integer…

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Q: Find the minimum distance from the point to the surface z = √4 - 2x - 2y. (-2, -2, 0)

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Q: need

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Q: Use Simpson's 1/3 rule with (n₁ = 2), and Simpson's 3/8 rule with (n₂ = 3) to estimate tan-¹(2).…

A: We have to estimate the given function.

Q: 7. Determine the intersection, if any, of the planes with equations x +y-z + 12 =0 and 2x + 4y - 3z…

A: Since you have posted multiple questions. As per guidelines we"ll solve only first first question.…

Q: USE NEWTON-RAPHSON'S METHOD IN FINDING ROOTS f(x) = ex²-2 + √√x + 2-3

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