Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) lim X-6 - (8 - 1—² x ) x) 3

Q: What is a solution of the first order equation Y (K+1) = Y(K) +5 ? Ans: y(K) = 20+5k

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Q: expr lim x→-8 -2x² - 20x - 32 x + 8 - 32)

A: Given problem:-

Q: 5. 1 Z+₁ 3z 2 dz

A: Topic = Integration As per guidelines , At a time only one question can be answered. please repost…

Q: B) Find the area between the parabolas x = y² - 1 and x = = 2y² - 2

A: We have to find area between the given parabola.

Q: Find dy dx 2. y tan-¹(csch x³)

A: Given y=tan-1 (csch  x3 )

Q: 3. Find the solution of the following systems of differential equations: (Nonhomogeneous) Use…

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Q: Use the Shell Method to compute the volume of the solid obtained by rotating the region above the…

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Q: If f(x) = x³ +1.5x² - 90x + 16, find analytically all values of a for which f'(x) = 0. (Enter your…

A: This question can be solved using the concept of differentiation.

Q: y sin(xy)dady csc²0d0dr ze-² drdydz (a) T/2 (5) [72² 1/2 π/2 ©fff (c) Jo Jo Jo

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Q: (D³ - 2D³ – 2D² – 3D − 2) y = 0 - - -

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Q: a=i+3j 2k, and b=i-3j-k, and c = 2ī+j-k, then...

A: Given problem:- a = i + 3j − 2k b=i - 3j - k c= 2ì + j − k  Then find v= 3(a - 2b +5c).

Q: 4. Evaluate the following integral using cylindrical coordinates: /16- *** z dz dy dr

A: A detailed solution is given below

Q: (3²+ 3a)dA, where D is the region in the 3rd quadrant between the circles 2² + y² = 1 and x² + y² =…

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Q: tersection point A rectangle is to be inscribed in an isosceles right triangle in such a way that…

A: A rectangle is to be inscribed in an isosceles right triangle in such a way that  one vertex of the…

Q: Consider the following. (If an answer does not exist, enter DNE.) f(x) = 2x³ + 3x² - 120x (a) Find…

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Q: Determine the centroid of the area bounded by the curves y = 4x + 16, x= -2, x = 5 and x-axis.

A: Given curves are,

Q: B. solve the following equation using Laplace transformation y' + y = sin(t) y(0) = 1

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Q: 3. Evaluate III 622 dV where G is bounded by r+ 2y + 4z = 8 in the first octant.

A: Use triple integral

Q: Find (3x + 4y)dA where R is the parallelogram with vertices (0,0), (-1,4), (-4,-2), and (-5,2). R…

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Q: ? Question Find the four distinct critical points of h(x, y) = x²y + xy² + x³y² + xy³. * Incorrect.…

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Q: Q5/ Solve the gamma function 2-3x² dx 360 A) 2√n 1 77 B) 2√3 In 2

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Q: Find the linear approximation of the function f(x, y, z)=√x² + y² + z² at (4, 7, 4) and use it to…

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Q: = If f(x) = f'(x) = ƒ'(5) = 4 tan x, then - sin(x)-4 sec² (x) Cos x

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Q: Use a linearization to approximate tan(π/100).

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Q: Use the graph of g to find the value of each expression. (If an answer does not exist, enter DNE.) y…

A: Given, Graph of g(x)

Q: 9. If the slope of the line determined by the points (x,5) and (1,8) is -3, find x.

A: Given that the slope of the line determined by the points (×,5) and (1,8) is -3. We have to find the…

Q: 7. Thirty two teams join a beach volleyball league. The league is split into four divisions where…

A: How many games should be scheduled in total for the league??

Q: Consider the following. (If an answer does not exist, enter DNE.) f(x) = ln(x² + 6) Find the…

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Q: For each of the transfer functions below, find the exact response of each system to a step input,…

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Q: - Find the mass of a lamina bounded by y = 5√7, z = 1, and y o(z,y) = x+2 0 with the density…

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Q: 2. v = e-sinx

A: Given

Q: Evaluate the indefinite integral. dx x(ln (x))6 (Express numbers in exact form. Use symbolic…

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Q: hand written plz Let A(0, -2), B(0,4) (1) Find the set of all points P(x, y) such that m(PA)=2.…

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Q: A farmer finds that if she plants 100 trees per acre, each tree will yield 45 bushels of fruit. She…

A: Here we will find the number of trees per acre to maximise harvest,

Q: Q.3) +4x+8 dx m a) tan-1/3+2 +c b) in 2 + c c)e()+c d)+c

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Q: 5 sin coso do 2 Sin ² + 3 sin 0 -4

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Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

A: The differential equation Mdx+Ndy=0 is said to be exact, if ∂M∂y=∂N∂x. The solution of the…

Q: A plane is defined by the equation x - 7y - 18z = 0. a. What is a normal vector to this plane? b.…

A: The given equation of the plane: x-7y-18z=0.

Q: 1. For what value of k if the line 6y +(2k-1)x= 12 perpendicular to the line 3y - 2x = 6

A: A line perpendicular to another has a slope that is the negative reciprocal of the slope of the…

Q: Consider the function F, that assigns x in its domain to x² - 1 F(x) = |x-1| In its domain. a. What…

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Q: Use the formal definition to find the derivative of g(x)=√6x at x = 3. Find g'(x) for the given…

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Q: dy dx = (1 + y²)ex dx

A: As per the instruction, we will be answering the first question. For (1),      y'…

Q: The waiting time T at a store counter is a random variable with exponential probability density. If…

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Q: 3. Erin, Catherine, and Shannon are dividing a large bag of candy. They randomly split the bag into…

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Q: Let R be the region enclosed by the curves y = x³ and y = 2x² The area of R using horizontal element…

A: The area of the region R enclosed by the curves, y=x3 and y=2x2 is given by Area=∫cdg(y)dy

Q: 2. Evaluate the double integrals by iteration. whre B is the region 0 ≤ ≤ 1, ² Sysz Jed da

A: Follow the procedure given below.

Q: 2. Find the area bounded by curves: b. x = 0 and x = 25 - y²

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Q: 12. [ xv2 − xdx

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Q: At exactly two of the labeled points in the figure below, which shows a function f, the derivative…

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Q: 5. The distance between the points (sin,cose) and (cos0,-sinė) is S

A: Distance between the points (X1,Y1) and (X2,Y2) is given by         ______________________ D =√(…