Let f(x) = { 2x-3. 3x²+2, if x < 3 if x ≥ 3 be a piecewise function. Evaluate Sof 0 f(x)dx=

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Q: Compute the line integral of f(x)=2x over the curve y=x² from (0,0) to (1,1). |

A: The line integral of f(x)=2x over the curve y=x2 from (0,0) to (1,1)

Q: an = arn+1 an = arn-1 * The general term of geometric progres Option 4 O anar" a" = arn-1 - Option

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Q: (a) (b) Evaluate S 9xsin (2-3x)XAMIMATION dx. *1*: FIDENTIA Evaluate 1 9x² +6x+ AL 123 CALCULU by…

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Q: Find the indicated derivative. 3 If f(x) = 24³x² + 96 3 VX find f'(8).

A: Here we will find f'(8),

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A: Given: Depth of pool = 10ft Area of rectangular plate, A = 3ft×4ft=12 ft2  Hydrostatic Force on…

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A: This question is based on application of derivative.

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A: Find the sum of the series (-1)n16n-2/(2n)! from n=0 to infinity.

Q: ey+5 | ey-5 ولا

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Q: Write the partial fraction decomposition of the following rational expression. 3x² - 8x + 20 X(X +…

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Q: For problems 1 - 16 use the method disks/rings to determine the volume of the sol the region bounded…

A: Here all question are not connected  According to bartley guidelines I am bound to solve only first…

Q: Find the area of a triangle PQR, where P = (6, 3, 5), Q = (0,4, -3), and R=(-6, -1, - 5)

A: As we know that; The expression for the area of the triangle PQR is: A=12PQ→×PR→   Given: P=6,-3,-5,…

Q: 4 T 40 sin(3x)dx None of them -0.532 -0.253 0.253 -0.235 0.0235 -0.325

A: Solve the definite integral

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Q: The United States population (in millions) is predicted to be P(t) = 317e0.01t, where t is the…

A: NOTE: Refresh your page if you can't see any equations. . the given function is  take derivative

Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

A: We have to analyze and sketch a graph of the function and find any intercepts, relative extrema,…

Q: Q1) Find the derivative a) f(x) = arctan (e-2x) b) f(x) = [arcsin (2²)]³ C) f(x) = tan (lnx) + 52²

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Q: 3. fx³√1 + x² dx

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Q: Sketch a graph of the function f(x) = 3 cos 6 5 4 3 2 1 -8п -7п -бп -5п -4п -3л -2л -π -1 -2 -3 -4…

A: This question is based on graphing a function from its principal function.

Q: A tank contains 240 liters of fluid in which 50 grams of salt is dissolved. Pure water is then…

A: A tank contains 240 litres of fluid in which 50 grams of salt is dissolved.pure water is pumped into…

Q: Find ln(9.2) from ln(9.0) = 2.1972 and ln(9.5) = 2.2513 by linear interpolation and get the %error.

A: We need to find ln(9.2)

Q: x² + y² = 7 X=7 O igular (solve) x² + y² = 49. - Option 1 O

A: Given that r=7  r2 =49 let x= 7 cos(theta) y=7 sin(theta)

Q: Prove the statement using the €, & definition of lim(x² + 2x - 7) = 1. →2

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Q: Numerically estimate the slope of the line tangent to the graph of the function f at the given input…

A: we can complete the table.

Q: The two vectors a = (-1,2,-4) and b = (2, -4,-8), are not parallel but are orthogonal. Select one: O…

A: Given vectors:- a=-1,2,-4 b=2,-4,-8

Q: If S then f(x)dx= 10 and is equal to Select one: O 10 05 015 O-5 [². [se none of the others f(x)dx…

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Q: The national debt of a South American country t years from now is predicted to be D(t) = 70 + 18t4/3…

A: Given that the national debt of a South American country t years from now is predicted to be…

Q: Find the derivative of the logarithmic functions: y = ln(12x-4)

A: Solution of given question is written in below steps.

Q: Question 10 Evaluate the following expressions. sin (tan-¹(√3)) cos (tan-¹(1))

A: By triangle property

Q: an +1 Suppose that an Σ απ( – 16)" gar n=1 →1 as n → ∞. Find the radius of convergence.

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Q: function. f(x) = 2x-3 Start by drawing the vertical and horizontal asymptotes. Then plot two points…

A: We have to draw the graph

Q: : Use the chain rule to find the derivative of w= x² + y² with dw with x = cost + sint, y = cost-sin…

A: This question is based on chain rule differentiation.

Q: 8 Find the sum of the series. Σ4¹/n-41/(n+1) answers. n=1 Give reasons for your

A: We have to find the sum of the given series.

Q: Let C be the curve y = 12 11 10 9 8 7 6 5 4 15 x³ 1 + 4 3x 25 Find the arc length of C shown above.…

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Q: OLA: Solve the following system by (method of inverse) 2x₁ + 3x₂ = 5 x₁2x₂ = -1

A: Given problem:- Solve the following system by (method of inverse) 2x1 + 3x2 = 5 x1 - 2x2 = - 1

Q: The value of the definite integral is Select one: 0 0 O 2/11 O-1/11 O none of the others O 1/11…

A: We have to solve above integral

Q: Let C be the curve y = 12 11 10 9 8 7 6 5 4 15 x³ 1 + 4 3x 25 Find the arc length of C shown above.…

A: Use arc length

Q: Evaluate the following integral. √144-16x² dx

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Q: Translate into English:  a. ∀x(E(x) ⇾ E(x + 2)).  b. ∀x∃y(sin(x) =y).  c. ∀y∃x(sin(x) = y).  d.…

A: Solution : Given that to translate into English

Q: Increasing global temperatures raise sea levels by thermal expansion and the melting of polar ice.…

A: Given L(x)=0.02x3-0.07x2+8x where x is the number of decades since 2000.

Q: A rectangle is to be inscribed in a semicircle of radius 7 cm as shown in the figure below.…

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Q: Q2: Fill in the blanks : 1- ff f(x,y)dydx represents the. 2- y" +(3y')5 - sinx = 4 of order 3-ye…

A: Since multiple questions are asked I am answering first 3 subparts

Q: The distance from the point K(3, -2, 0) to the xz- plane is Select one: O-2 O √13 O 0 02 None of…

A: We need to find out the distance between the given point and xz plane.