A) If (xn) is a decreasing and bounded sequence. Prove that (xn) is convergent with lim xn = inf {xn nE N} %3D

Q: (a) f(x) dx 10 15 (b) f(x) dx

A: Here we have to find the given integral using the area under the graph

Q: Use the chain rule to find dy/dx for th following (a) y= (3x^2 - 13)^3

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Q: Use the triple scalar product to find the volume of the parallelepiped hav u = i+j v = j+ k w = i+k

A: Given: u=i+kv=j+kw=i+k

Q: Find the distance between the parallel planes – 2x + y + z = 0 and бх — Зу — 32 -13 — 0. %3D

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Q: Consider the following function. f (x, y)  =  (x − 4) ln(x6y) (a) Find the critical point of  f.…

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Q: Find the area between the curves y=e−0.2xy=e-0.2x and y=1.6x+1y=1.6x+1 from x=0x=0 to x=4x=4.

A: Given query is to find the area under the curve

Q: 3. According to Newton's cooling law, the rate of cooling of a hot body is pro- portional to the…

A: According to Newton's law of cooling, we have T(t)=Ts+(T0-Ts)e-ktwhere T(t)- temperature of body at…

Q: Determine whether the sets S, and S, span the same subspace of R. s = ((0, 0, 1). (0, 1, 1), (8, 1,…

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Q: х3+9х2+20х 4. lim х-3+ х2+x-12

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Q: Perpendicular to the plane z + 3y – x = 7 and containing the points (2, 5, 0) and (0, 2, -1)

A: Solution of question is written in below steps.

Q: Evaluate the limit. (Use symbolic notation and fractions where needed.) 14/3 lim + 7t/3 (3123 + 13)²

A: Given query is to find the value of the limit.

Q: it. notation and fractions where needed.)

A: We have to find the value of the given limit according to the rule of limit

Q: Given that Vf(11, –6) = 10i – 8j, find the directional derivative of the function f at the point…

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Q: Quest An exercise machine with an original price of $970 is on sale at 10% off. a. What is the…

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Q: dy = x and find the particular solution when y(0) = dx Solve y? %3D

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Q: Find two unit vectors in 2-space that make an angle of 45° with 10i + 3j. NOTE: Enter the exact…

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Q: Evaluate the following integral using the method of partial fraction. (2х3-3х?) dx a. 2x2-7x+5

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Q: S 4x cos(2 – 3x) dx

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Q: f. lim f(x) if f(x) = |x² – - 2 if x > -1 1/x g. lim f(x) if f(x) : if x -1 x +3 if x 1

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Q: Perpendicular to each of the planes x – z+ y = 0 and 2x + z – 4y = 5 and containing the point (4,…

A: We have to find an equation of the plane which is perpendicular to each of the planes x-z+y=0 and…

Q: termine the area bounded by

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Q: Evaluate the following integral using trigonometric substitution. dx b. S- (5+2x+ x²)5

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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Q: (the trace of A). Prove that T is a linear transformation. Let A and B be to matrices in M, and let…

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Q: Solve the differential equation by variation of parameters. y" + 3y' + 2y = cos(e*) y(x) =

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Q: Find two unit vectors in 2-space that make an angle of 45° with 7i+ 6j. NOTE: Enter the exact…

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Q: 11) The Inverse of ()= *-1* a)(x) 3x-1 b)/(x) log2(x) d)f(x)= log3(Vx+1) e) non

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Q: Suppose f( – 1) =7, f'(– 1) = 4 , and g(x) = r°f(x). The tangent line to g(r) at z = 1 is given by Y…

A: Given: gx=x3fx, f-1=7, f'-1=4   The expression for the equation of the tangent line is: y-y0=mx-x0…

Q: Differentiate the following using logarithmic differentiation. Vcos? x*(x-1)3 3. y = %3D (x+vx)

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Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i, j…

A: To find the unit vectors that satisfies the given conditions.

Q: Please solve the problem using the Substitution Method. Thank you!

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Q: Find the ff: a. if the differential equation in question is linear b. the given differential…

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Q: X Your answer is incorrect. Find an equation of the plane that passes through the points (-2, 1, 1),…

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Q: Show that the lines L1 : x = 2 – t, y = 2t, z =1+t and L2 : x = 1+ 3t, y = 3 – 6t, z = 5 – 3t are…

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Q: Question 2 Jordon currently has a shipment with the below details: The shipment has two types of…

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Q: The following Riemann sum gives the Right-Endpoint approximation of the area under the curve of some…

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Q: GIVEN : 2x 2х - 2x ) + 6 1 1 f (x) = 1 --x 8 g(x) = 3(x + + 4 h(x) = 6 - || 3 a.lim -4 · f (x) d.lim…

A: For (a),     limx→2-4 f(x)=limx→ 2-41-18xPlug in the value x=2=-41-18· 2=-3

Q: 3. y" +3y" + 3y' ty :e-x - ylo) =o yto y" lo) y" la)= 2

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Q: Use the quotient rule to prove the derivative of: [Hint: change into sin x and cos x a I. tan x 2.…

A: As per our guideline we are supposed to be answer only three subpart of question you can repost…

Q: The graph of a function f(x) is shown below. If the definite integral | f(2)dz gives the area of the…

A: Given query is to find the area under the curve.

Q: Use vectors to find the lengths of the diagonals of the parallelogra that has i + j and i – 18j as…

A: Given query is to find the length of the diagonal.

Q: n equation of the plane with the given characteristics. y – 4 The plane passes through the point…

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Q: Solve the differential equation by variation of parameters. 2y" — 4y' + 4у %3D е* sec x y(x) = %3D

A: Solution is given below:

Q: Find the slope of f (x) = 2x2 – 5x + 6 at (3, 9). Use a graphing utility and round to the nearest…

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Q: Solve the initial value problem below using the method of Laplace transforms. y" + 9y = 18t - 18t…

A: Let's find.

Q: Find the directional derivative of the function at P in the direction of v. h(x, y, z) = xyz, P(8,…

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Q: where k > 0. 4. s(s-k)'

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Q: xvx – 1 dx. | 1

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Q: A snowball is thrown upward from a bridge into a river below. The function f(t): above the surface…

A: f(t)=-16t2+47t+88t=0f(0)=88gives the bridge's height.Brige's height =88 feetB)When the snowball hits…

Q: Determine whether the lines L, and L2 are parallel. L1: x = 1– 4t, y = 2 + t, z = 4 – t L2: x = 4 –…

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