Find the exact length of the curve. x = 5 + 12t², y = 6 + 8t³, 0≤ t ≤ 3 12117-1)

Q: 164. A small town in Ohio commissioned an actuarial firm to conduct a study that modeled the rate of…

A: NOTE: Refresh your page if you can't see any equations. . the population(in thousand) of the town…

Q: 3. Find lim f(x) and lim f(x) for the given function and value of c. Tough X-C+ X-C f(x) = (x+8)-…

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Q: Obtain the differential equation whose general solution is y = ₁ + ₂³x A. B. |y" - 3y' = 0 D. E. 3y"…

A: Differentiate both side with respect to x

Q: Use synthetic division to determine if the given value for k is a zero of this polynomial. If not,…

A: By using synthetic division method the solution of given problem is as follow

Q: what is increasing function?

A: Increasing function It's constantly rising. The trail we're on occasionally slopes uphill,…

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: 5. Let f(x) = 4x2x3 - 1. Explain, by using the Intermediate Value Theorem, why this function has (at…

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Q: The integrating factor (IF) of the equation y' - 2ycot2x OA. sin2x OB. cot2x O C. Lnsin2x OD. CsC2x…

A: To find the integrating factor IF of the following equation,y'-2y cot2x=1-2x cot2x-2 csc2x

Q: Which of the function is not an exact equation of the first order? OA. (ey + ycosx)dx + (xe³ + sinx…

A: See this solution in below.

Q: Which of the following equations has a solution of the form F(x,y) = C A. 2x + 3y + (2y + 3x) dy =…

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Q: Question 27 The integrating factor (IF) of the equation: (2x³y² + 4x²y + 2xy² + xy² + 2y)dx + (2y³ +…

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Q: indi the derivative  y=arctan² (x³)

A: Given,   y=arctan² (x³)    Find derivative of y

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

A: Option D

Q: Evaluate the piecewise function at the given values of the independent variable. h(x)= (a) h(3) x² -…

A: The function is given by hx = x2-36x-6if x≠65if x=6 To evaluate: The values of a h3  b h0  c h6

Q: Let f(x)=−3e^x+2+e^4 f′(0)=

A: SOLUTION-

Q: Given the vectors à = (2, -1,3), b = PQ where P(1, 1, 1) and Q (5, 1, −1) and Ĉ=i+j+ 3k. Find a)…

A: Given the vectors a→=2, -1, 3, b→=PQ→ where P1, 1, 1 and Q5, 1, -1and c→=i→+j→+3k→.To find 7b→-3c→

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

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

Q: the following function. y = x³ + 3x² - 9x + 3 ~'(x)..

A:

Q: Can someone compute this into decimal form. f'(4)=-sin(4)-3sec²(4) Thank you

A: we already have f'(x)=-sinx-3sec²x so,f'(4) =-sin(4) -3sec2(4)

Q: 13. Suppose that lim f(x) = 13 and lim g(x) = -7. Find the following limits. X-4 X-4 a. lim…

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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 expression, y=x3-12x

Q: A distribution of values is normal with a mean of 22.3 and a standard deviation of 41.1. Find the…

A: Given that a distribution of values is normal with a mean of 22.3 and a standard deviation of 41.1 .

Q: Find the y-coordinate of the point (a + 1, ?) if this point lies on the graph of the function f (x)…

A: Given: f(x) = x3 The points are: x = a+1 y =? Formula Used: a+b3 = a3+3a2b+3ab2+b3

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: The rate of change of the variable y in terms of another variable t is equal to the expression 5t4 -…

A: Your option is incorrect but my solution is correct .

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: fxe* dx.

A:

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: 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: 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: (2) fx sin 2x dx.

A:

Q: The integrating factor (IF) of the equation y' - 2ycot2x = 1-2xcot2x - 2csc2x

A:

Q: dP Which among the choices is the same as the differential equation = P(C₁ - C₂P)? dt A. OB. dP dt…

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Q: Find the general solution of the differential equation y" + (wo)²y = cos(wt), w² ‡ (wo)². NOTE: Use…

A: Solution: Given data, y"+(w0)2y=cos(wt) Lets compose the auxiliary equation m2 + w02  =0 m1 = iw0 m2…

Q: Which of the following equations is NOT a variable separable differential equation? A. 2xydx + (x² +…

A: A Separable differential equation is any equation that can be written in the form of dydx =…

Q: Evaluate the following integral. 9 4 dx 1-√√x

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Q: 10. Find the first 3 derivatives of f(x) = √√x. Evaluate the function and the first 3 derivatives at…

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

A: Given a  equation of general solution of a differential equation. By terminating arbitrary constant…

Q: 111 Solve for the actual solution of y''' = 2x + 1 when y(2) = 1, y'(2) = − 4, y''(2) = 7 X 12 6 X 4…

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Q: Consider two lines. Line L1 is defined by 1, and Line L2 is defined by y = 3x y = 2x + 4. A. Without…

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Q: 5. Show that dy ay of dx of arccosx -1 √1-x²

A: Given that dydx of arccosx=-11-x2 We have to prove this derivative.

Q: Which of the following is a non-homogeneous function? tan³y/x xLnx − xLny - xy + y² (y² + v²)3/2 43…

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Q: dy What is the IF for solving the linear equation: x dx O O O O A. 3 X2 B. 3x 2 C. 3 -Lnx D. E. 3x e…

A: It is linear differential equation

Q: 7. Find (a) the slope of the c y=9x² -1; P(4,143) (a) The slope of the curve (Type an integer or a…

A: solution:-y=9x2-1slope= dydx=ddx9x2-1=18x(a)slope of tangent at point P(4, 143)slope = 18(4)=72

Q: Find the following matrix product, if it exists. -5 - 5 135 O A. -5 Select the correct choice below…

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Q: 16. Find the limit of the following rational function as (a) x-∞o and (b) x--co. -2x²-3x²+2 7x³+2x²…

A: Limit

Q: 1. y arctan² (x³) =

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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: Question 26 Solve for the value of constant C in the equation: (2x + 3)y' = y + (2x + 3)¹/2 when x =…

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Q: What is a suitable integrating factor that can be used to solve the equation dy +2y-4xy-e* cos(2x) =…

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