Use limits to determine all the linear asymptotes of 3x2 – 5 if a<1 272 +x f(x) = if r>1. a² + 2x – 3'

Q: 9t + 8 dt t

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Q: I = -2+3s z + 4 1. Consider the lines defined by the equations l : x – 2 = y – 1= and l2 : y = -1+ s…

A: Given:  l1= x-2 = y-1 = -z+42=tl2= x+23 = y+1 = z-2-4=s

Q: Find an equation of the plane through (0, -9, – 1) that is perpendicular to the line x - 2 = 3t, y +…

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Q: Medicine The graph shows the estimated number of milligrams of a pain medication M in the…

A: Given: The graph shows the estimated number of milligrams of a pain medication M in the bloodstream…

Q: Solve the equation: (2r – xy? – 2y + 3)dx – (x²y + 2x)dy = 0 x4 – 2ry? – 4xy + 6x = c O x* - x²y² –…

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Q: Give the curve r = 3 cos 0 b) Find the points on the given curve r = 3 cos O where the tangent line…

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Q: 3- x 3) dx → S2xe* dx

A: To evaluate the given integrals.

Q: Find u v, u·u, ||v||², (u · v)v, and u · (3v). (5, -2, 4), v = (0, 7, 5) U = (a) u V (b) (c) ||v||?…

A: The given vectors,  u=5,-2,4, v=0,7,5

Q: Find the area of the region between the graphs of f (x) = 3x3 – x² – 10x and g(x) = -x2 + 2.x, %3D -…

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Q: Consider the following. u = (6, -1, 0) v = (-2,3,0) Find u x v. Determine if u x v is orthogonal to…

A: Explanation of the answer is as follows

Q: Homogeneous or not? State the degree of function if homogeneous. x^3-xy+y^3

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Q: d?y +5xy = 0 dx +(sin x) 2 dy +2 dx dr3 = 1 dx2 O Option 1 O Option 2 d²y +3y dy dy dx? +y = 5x dy…

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Q: Given the series: k=0 does this series converge or diverge? O diverges converges If the series…

A: The given series is ∑k=0∞-16k. To check convergence of the series we use ratio test. Suppose we have…

Q: Verify that the two planes are parallel. -x + 6y + 3z = 8 1. x + 2y + z = 9 Find the normal vector,…

A: Let's find.

Q: (0,0,0) (1,1,1) C2 C.

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Q: 4- x2 Evaluate lim x+2 3- (x2+5)Z 5 3 O NONE OF THESE O 4

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Q: (b) Find the distance from D to the plane containing A, B, and C. NOTE: Enter the ezact answer.…

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Q: Eliminate c from the equatia cxy + c²x + 4 = 0. O x* (y')? + x?yy + 4 = 0

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Q: 3) Given f(x) =-2x -2x-2, find the absolute maximum value over the interval [0,6].

A: We have to slove the above question and find absolutely maximum value

Q: The limit of a constant is always a constant. O FALSE TRUE

A: To proof the limit of a constant is always a constant. Let the function fx=k, here k is a constant

Q: Compute the first four partial sums S1, .., S4 for the series having n th term an starting with n =1…

A: In this question we have to find partial sum.

Q: d) Producers' Surplus (Round all values to the nearest integer and do NOT use commas or dollar…

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Q: If e = then %3D 4. sin(0) = %3D cos(0) = Give exact values. No decimals allowed!

A: Follow the procedure given below.

Q: Determine if the sequence is increasing, and/or bounded. 3 — п (b) { (a) 1 — Зп - 3n n=1

A: Given

Q: Consider the following. 3D(6,-1,0) v = (-2, 3, 0) u = %3D Find u x v. Determine if uxvis orthogonal…

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Q: Given the pair of price-demand and price-supply equations below, calculate each of thne following:…

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Q: 1. Consider the graph of the function f(x) = 1.a. Is the function f (x) continuous at x = 1? Justify…

A: We need to find if the function is continuous or not in given interval.

Q: 1. Find and classify the critical points of the following functions. (a) f(r,y)=+ - y %3D (b) g(x,…

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Q: a) | f(x)dx = b) | f(x)dx = c) 5f(x)dx =

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Q: 6) (7 tarr-3/2 x secdx dx

A: Here we have to solve the given integration.

Q: Consider the following differential equation. (x2 + y2)y′ = y2 Let  f(x, y) =  y2/x2 + y2 .  Find…

A: This is a problem of differentiation of the function. Based on the general formula we will answer…

Q: 4. S ( 12 x³ + 15 x - 20 ) dx 5. S 10 x2/5 dx 6. § 3 ³V x8 dx 7. S ( 8 + 2 dx x3 x4. 8. S ( 2x³ -…

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Q: (e) Alternating Series Test: Σ (-1)"-2 3n + 3n

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Q: Find the vector v with the given magnitude and the same direction as u. Magnitude Direction V -6…

A: This is a problem related to vector calculation. Based on the general formula we will answer the…

Q: 5- 3x? Evaluate lim x-00 (2-x) (x+ 2) does not exist O NONE OF THESE -3 3 O O o O O

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Q: Calculate the work done by the field F when the object moves along the given path from the initial…

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Q: Find r'(t), r'"(t), and r'(t) · r"(E). r(t) = (t2 + 7t)i – 2t?j (a) r'(t) (b) r"(t) (c) r'(t) ·…

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Q: -1 8 - 2 Use this procedure to find the inverse of A =| -6 49 -4 34 -5

A: We can solve this as follows:

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

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Q: 1 у 3 2 y (х + 2)

A: y = (x+2)-1/2 dy/dx = (-1/2)(x+2)(-1/2 - 1) dy/dx = (-1/2)(x+2)(-3/2) dy/dx = -1/2(x+2)3/2

Q: Find the area of the region enclosed by the rose r= 20 cos 30. NOTE: Enter the exact answer. A %3D

A: Solution is given below:

Q: Determine whether the given series converges or diverges. 4n – 8n 5" n = 1 converges O diverges If…

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Q: Find the arc length of the parametric curve. x = e', y = et, z = v2t; 0<t < 8 L ||r'(t) × r"(t)||…

A: Given parametric curve x=et  , y=e-t  , z=2 t   ;  0≤t≤8

Q: e2x :dx /1– ex

A: Given:        ∫e2x1-exdx  substitute u=1-ex→dudx=-ex→dx=-exdu  use e2x=1-u2      =∫u-1udu Expand:…

Q: The world population at the beginning of 1990 was 5.3 bilion. Assume that the population continues…

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Q: 2(у - 4x?)dx + хdу %3D 0. x²y = 2r* + c

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Q: xe* хе dx. J (x + 1)2

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Q: Find T(t) and N(t) at the given point. r(t) = (t² – 8)i + tj; t= 8 %3D T(8) = | %3D N(8) =

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Q: Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8); fi-) U =

A: we can solve this as follows:

Q: Examples: Find the limits of the following: 1. lim sin x = sin1 = 2 5. lim sec x = lim cos(-) = cos0…

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