Which of the following is the general solution of the differential equation y" - 36 y=0 ? O y=d,ex+d2xe¬6x O y= (d,+d,x)e°x* O None of them -6x O y=d,xex+d,e O y=d,ex+d,e -6x

Q: inside polar functionr = 2 and outside p in third auartor

A: We have to find the area according to the given information

Q: Q2) Convert the polar function r tan20 to cartesian.

A: We have to convert polar equation into Cartesian equation

Q: (x – y)dr + xdy = 0.

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: 2x 4. Given the function F (x)= 3 do the following: 4.x +1 a. Find F-1 (x). b. Find dom F and dom…

A: Given,            The function is Fx=2x-34x+1.

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Q: Evaluate +V7dx 3 Oa.5 +C 2 5 3. Ob.2 3 2 Oc 2 sm +- Ot ast Od +C 3 2 52~

A: Evaluate integral

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A: We have to check whether the given statement is true or false.

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Q: Question 3 2 dr sech 2r = A True B) False

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Q: (x-2)" En=0 n2+1 n3D0

A:

Q: 4. Find the Laurent series of the following function : f (z) = (z + 1)(z + 3) 1 region 2 < |z – 1| <…

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Q: What is 2x4

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Q: Solve the particular solution of the equation dy/dx = 3x² - 2x, when y=2 and x=-1.

A: We can solve the given problem as follows:

Q: Learning Competency: illustrate an antiderivative of a function. Question Is S Gx2 + 5x + C)dx = 3x…

A: Given,             Is ∫32x2+5x+Cdx=3x+5 correct.

Q: Consider the parametric curve defined by x=3+5t and y=1+3t Over which values of , does the curve has…

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Q: Find h'(x) if h(x) = x³e*sin x. O a. h'(x) = 3xe*sin x + x'e*sin x + x'e*cos x 3X, O b.h'(x) =…

A:

Q: Q2) Evaluate the following integral using Trigonometric Substitutions Method: dx y 9x² + 16

A: To evaluate: I=∫dx9x2+16 Substitute x=4sec u3⇒dx=43sec u tan u du

Q: dy = Solve 2xy r x2 + y? given that y = 0 at a = 1 %3D

A: To find particular solution of D.E.

Q: 6.Find all the first partial derivatives of each function x² – y² c. f(x,y) ху с. = d. f(x,y)=e* cos…

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Q: Differentiate the following function and factor fully. g(x) = (2x – 1)*(2 – 3x)“ |

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Q: Find the centroid of the region bounded by the parabola y= 8x and the line y=2x. O (0.8,2) O (1,4) O…

A: We need to find centroid of the region.

Q: Q2) Convert the polar function r tan20 to cartesian.

A:

Q: Q3/ Solve the following equation by (Finite Difference Method), choose (h= 0.5) *+ 2y = 3 ,y (0) =…

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A: Given problem:- Egay wants to fence a rectangular grazing area along a straight river (no fence is…

Q: (a) Show that the integral test applies, and use the integral test to determine whether the series…

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Q: Q5/ Use Linear Regression to fit the following data: 1 4 5 6. Y 4 9 10 10 9 8 3

A: From given data

Q: wolloi or oisuleu 6. (-3x+15x") dx 12x 15 12 dx 7. + 3 x'

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Q: 1. Mang Vicente has 1000m of fencing material and wishes to enclose a rectangular field. Two (2)…

A: Mang Vicente has 1000 m of fencing material and wishes to enclose a recangular field. Two adjacent…

Q: Express the shaded area of the region shown below by double integrals of order of integration (1)…

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Q: Find the value of t for which 1 V3x+1 O none of the choices 6 O 3 O 5 O 4

A: Here, given that: ∫1t13x+1dx=43

Q: Consider the solid bounded by the planes: =x+y, z=30, x=0, y=0. Determine the volume of the solid.

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Q: 2 dr sech 2r= e2r +e-2r A) True B) False

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Q: Find the two x-intercepts of the function f and show that f'(x) = 0 at some point between the two…

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Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

A: Let's find.

Q: Evaluate the definite integral. e12. i+ k 12 e12 i-elj+; k 12 e12 -1 12 e12. k 12

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Q: Let a = 2i - 3j and b= 2j + 3k. Compute for the following: (a + b) · (a – b) None of the choices -8

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Q: tan²x dx, can be evaluated by using trigonometric transformation . A True False

A: The given integral is: I=∫sec5xtan2xdx Use the derivarive: ddx(secx)=tan2x

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Q: Find an equation of the sphere whose diameter is the line segment having endpoints at (6,2, –5)

A: To find the equation of sphere.

Q: Q3) Evaluate triple integral f Lx - y²)dz dy dx.

A: The given problem is solved below in detail.

Q: None c) cosh x + C sinh x +C 2 sinh x +C cosh x +C

A: The given integral,      12∫ex-e-xdx

Q: applying substitution méthöd: sqns -48

A:

Q: | sinh54x cosh 4x dx can best be evaluated by General Power Formula. A True В False

A: Option A is true

Q: –6x-'dx

A: Follow the procedure given below.

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A: