Evaluate the definite integral. 8 [x√x - 7 dx 5.06

Q: -2 Evaluate: ²₁²[(x²-²²] 0 x+y du dt

A: Topic = Integration

Q: ) Find the area of the region bounded by y = ex, the x-axis and the y-axis.

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Q: 6. I. Evaluate each determinant. тут 3-3 4 1 0-1 -1 -4

A: Given data

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Q: Set up the triple integral that will give the following: the volume of R using cylindrical…

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Q: Find the general solutions for these differential equations: a. xy’ (2y - 1) = y (x - 1) b. (xy –…

A: We have to solve given D. E.

Q: 4 Find the area of the region bounded by x = 2y²+1 and the y-axis using the horizontal strip.

A: Given: x=42y2+1

Q: The derivative of y with respect to given a = 1 is Onone of the choices O y = yx³-1 O V = 0 = = 9 *…

A: I have stated the used formula in the solution

Q: 1. Perform the following integration. 1. | (sinh a)(coth® a + cscl® a) da

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Q: Determine how the function f behaves at infinity. f(x) = (x³∕2x³) + (2/5x) -2

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Q: I. 2.) Simplify. Write "undefined" for expressions that are undefined. 5 3 2 I(1J + -6 -6 2 0 2

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Q: Evaluate the integral: .0 ²/3 t ln u tan s ds du dt 2e π/3

A: Given: ∫-10∫e2e∫0π3t lnu tansdsdudt

Q: Find the area of the region bounded by the curves y = 1 (x+6)²¹ y = 4 and the x-axis using vertical…

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Q: Solve the differential equation dx 4x+6y+5 - dy 3y+2x+4

A: Concept: The general form of non-homogeneous differential equation  dydx=a1x+b1y+c1a2x+b2y+c2 Check…

Q: For the following exercises, use the second derivative test to identify any critical points and…

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Q: I. Simplify. Write "undefined" for expressions that are undefined. -1 5 -3 6 3 3.) 5 0

A: We have to find out product

Q: I. 1.) Simplify. Write "undefined" for expressions that are undefined. 2 [164] -6 -5

A: Topic = Matrix

Q: ع لح ل(۸ + ")APNPLPLg للع(۸

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Q: 3 f²f²² ²³ y cos(z³) dx dy dz 0

A: The given integral:∫01∫0z2∫03ycosz5dx dy dz

Q: The value of A. +3+2x² +C C. = + x² +2+C 20 [ (² + 3) *²x² dx B. +³²+3x³ + C 28 D. none of the…

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Q: -3 -t Evaluate the integral: Soft²eu du dt е

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Q: (1) Let I be a proper ideal of the commutative ring R with identity. Then I is a ........ if and…

A: 1) Let I be a proper ideal of commutative ring R with identity. Then I is a ............. if and…

Q: derivative of (√2)^csc4x

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Q: cln s Evaluate the integral: St² főr teu du ds dt

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Q: Q1/ Without using L'Hopital rule, find the following limit. √2+x-√2-x lim- ×-0

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Q: Determine the intervals on which the function is concave up or down and find the points of…

A: topic- inflection points and concavity

Q: Evaluate the integral: -2e π/3 ₁²/³ tlnu tans ds du dt

A: Topic = Integration

Q: Evaluate: ³₂(4x²y - 2³) dz dy dx

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Q: A stone, projected vertically upward with initial velocity 112 ft/sec, moves according to s = 112t -…

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Q: Solve for C using the form f(x,y)=C. Given [2x + ycos(xy)] dx + x cos(xy)dy = 0; f(1)-pi/6. decimal…

A: differential equation

Q: (1+y^2)dx+(x^2y+y+2xy)dy=0

A: 1+y2 dx+x2y+y+2xy dy=0

Q: v²dx + x(x + v) dv=0 O xv² = c(x+2v) Ox²v² = c(x + v) X V 2 Oxv² = c(2x + v) O xv² = c(x + v)

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Q: 2 -1 4 4 -6 1 -3 -5 北

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Q: 1. Evaluate the assigned limit using L'Hopital's Rule. lim [cos (2x)]¹/(*-*) X-T

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Q: If the total cost function is given by TC = 300 + 5g + 3 then the marginal cost function MC = O a.…

A: We have to find the marginal cost function.

Q: = Find the area of the region bounded by x = and the y-axis using the horizontal strip. 4 2y²+1

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Q: 3 Evaluate: (4x²yz - z dz dy dx 24

A: The integration of the triple integral is (4x2yz-z4/4), z from 0 to 1, y from -1 to 4, x from 2 to…

Q: -2 Evaluate the integral: ² ft² n s teu du ds dt

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Q: 2. The Substitution Method states that A. If F'(x) = f(x), then [ f(u(x))u' (x) dx = F(u(x)) + C B.…

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Q: ways

A: Please refer to the image below

Q: For the following exercises, use the second derivative test to identify any critical points and…

A: Given :f(x,y)=-x2-5y2+10x-30y-62

Q: Determine the values of r for which the differential equation y + 2y = 0 has solutions of the form y…

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Q: cos x(sec x + tan x)dx

A: Given ∫cosx(secx+tanx) dxTo evaluate the integral:

Q: Find the transition points. y = 9x6 - 81x4 (Use symbolic notation and fractions where needed. Give…

A: This question can be solved using the concept of maxima and minima.

Q: What will be the orientation of the curve of the graph of the function f(x) = 3 on (-3,0)? z² z+3 O…

A: Given the function  f(x) = x2x+3 on -3, 0.

Q: Apoint P(x,2) is equidistant from the points (-2,9) and (4,-7). What is thevalue of x?

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Q: Z4 e: 2₁₁ (4x²yz - ) dz dy dx 1 4

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Q: e: √₂² ²₁₂₁ (4x²yz - ²) dz dy dx 4

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Q: The value of A. - 3 cos (1²/³) + C C-3 cos (¹/3) + C sin(1¹/3) dt

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Q: (x² - y²)²] 1²₁ 1² du du dt x+y Evaluate: ₁ S

A: Given ∫-13∫02x2-y22x+ydudt Since x2-y22x+y is constant with respective u and t, we take constant out…