5 If [F(x) dx f(x) dx = 7.4 and 1.°F(x) dx f(x) dx = 5.7, find [²1 f(x) dx.

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Q: 46. Evaluate the definite integral (3x² - 4x - 5)² (6x-4) dx. 81

A: As per our guidelines we are supposed to answer only one. Kindly repost others question as a…

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A: Slope of the Normal line to the curve f(x) is -1f'(x).

Q: 62. du * |x|dx

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A: Given that  cosθ = 15 and θ is in quadrant IV. We have to find the value of  sinθ.

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A: Please read whole answer your doubt will be cleared.

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Q: Find the laplace transform of f(t)= t²e³t sin 4t OF (s) OF (s) = OF (s) = OF (s) = OF (s): - OF (s)…

A: This question is related to Laplace transform, we will solve it using given information.

Q: 1+tan x

A: We have to find the integral.

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A: This question can be solved using the concept of dot and cross product of two vectors and…

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A: To calculate area under curve we have to integrate the function within the given limits Please note:…

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Q: Solve the following differential equations of d²y_2dy + y = 2x dx² dx

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Q: Solve the given differential equation. All solutions should be found. dy 3x² - 7y - y³ 7x + 3xy² dx…

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Q: d (h) (cot ¹(2)) = d (i)=(sec ¹(1))= = d (j) (csc-¹(2)) = dr 1 du 1+² dz 1 du I√²-1 dz 1 du I√²-1 dr

A: Given problem:-

Q: V. Given: if x ≤ 2 el3r-6-2, [2x - 5], 13 f(x) if 2 3 √x²9, 1. Determine if f is continuous or…

A: Solution is given below:

Q: Evaluate the following. √(x²-2) e¹-6x dx

A: Use substitution method to solve the integral.

Q: Consider the vector Field 7 and the curve C below. F(x,y) = (3 +4 ху?) 1 + 4x²yј, C is the arc of…

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Q: II. Find Do not simplify your answers. 1. log, (2x² + y) + tan(x − ³) = sin−¹(x² − 1) +

A: Given problem:-

Q: a. (7+7i)(i + 1) UNA 7+7i i+1 C. (727°) (121°) e b.

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Q: Integrating Factor by Inspection: 3. xdyydx = 3x²(x² + y²)dx

A:

Q: II. Find Do not simplify your answers. da 1. log, (√2x² + y) + tan(x² − ³) = sin¯¹ (2² − 1) + 2

A: log3(2x23+y )+tan(xπ-πy)= sin-1(x2-1)+π21log(3). 2x23+y 23×23x-13+y'+sec2(xπ-πy).(πxπ-1-πy.…

Q: -2 + อน Ore 0

A: Suppose uxy=0 , denotes u = uy implies uy = 0 uxy = F(x) + G(y)  ,satisfies uxy = 0 a) y du/dxdy +…

Q: 2. y = tan-¹(cosh x) (sin² x) (sech x) secx [use logarithmic differentiation]

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Q: y = 2 x + 2 -3+x

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Q: V. Given: 2. Find f'(2), if it exists. f(x) = el32-61-2, [2x - 5], √x²-9, if x 3 14

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

Q: Find the area of the region bounded by    x2 = 4 - y    and     y = x -2  Hint: use Vertical strip.

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Q: Locate the absolute extrema of the function on the closed interval. f(x)= x³ 12x, [0, 4] -

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Q: A courier service will deliver a package only if the length plus girth does not exceed 108 inches.…

A: Use the application of derivative and find the maximum volume.

Q: Use the information to find and compare Ay and dy. (Round your answers to four decimal places.)…

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Q: Question 2. Determine the equilibrium price(in hundered rand) and quanity (in thousand units) of a…

A: Find your answer below

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Q: Use the function to find the image of v and the preimage of w. T(V₁² V₂) = (V₁ + V₂₁ V₁ V₂), V =…

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Q: An object moving along a horizontal coordinate line has directed distance s(t) = 4t³ +9t² - 30t + 5…

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Q: Solve the following differential equations of y" +4y'+3y=3e²x;

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Q: 1. Identify the equations of all the linear asymptotes of f.

A: There are three different types of asymptotes for a function fx: (i) Horizontal asymptote: If we…

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A: Use the ratio test for checking the radius of convergence of series

Q: if any. Find the absolute extremum point (s) of f(x) = el-cosa on [-, ],

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Q: 60. (a) dx SI dt 1 + √t (b) de fint di dt

A: We can solve this as follows:

Q: [w (1-32)] 3w 11. lim w In 1 In W→∞

A: LetL=limw→∞ wln1-23wFor L hospital L=limw→∞ ln1-23w1wNow apply L hospital ruleL=limw→∞…

Q: d'y dx² d²y + dy dx X=

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Q: b. 36. Evaluate f(4x³ - 9x5 + 4x² - 6) dx. a. 32x7-45x + 8x + C 32x7 180x³ 4x9 C. b. 3 +8x + C…

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Q: Solve the DE ý - y = x

A: See the details solution in below

Q: d Calculater₁(t) r₂(t)] and [r₁(t) × r₂(t)] first by differentiating dt dt the product directly and…

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Q: Determine whether the equation is exact. If it is exact, find the solution. If the differential…

A: