1l aependson the ding exists entory model I-4x 56. lim +-00 X + 55. lim X 9x+ 5 7x4 ost, assuming of units sold 58. lim 57. lim ear, s is the s per order. 3x2 60. lim 59. lim XLI8X+5 2x nse D (in own in the ponding to lget) 5 COSX 62. lim 61. lim +2 X-Loo X 6x 64. lim X-o sin x 63. lim APFinding Horizontal Asymptotes Using Technology In Exercises 65-68, use a graphing utility to graph the function and identify any horizontal asymptotes. 5x2 3 65. f(x) 66. g(x) +4 4x2-1 68. f(x) 67. f(x) = 8x+ 1 o find Analyzing the Graph ofa Function In Exercises 69-78, analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. del. 70. f(x) = x4 -2x2 + 6 69. f(x) = 4x - r del 72. f(x) = (x -4)2 71. f(x) = x16 - x2 74. f(x) (x - 3) (x + 2)3 73. f(x) x1/3(x+ 3)2/3 5- 3x 2x 75. f(x) 76. f(x) el 1 + x2 1 78. f(x) = x2 + 77. f(x) = x3 +x + x 4/

Q: f'uo) -22:2294 W = 0.4748 2nd Stetzation flui) = fla4748) = 31e flui)= 0.0044 f'ni)= flouT48) = -31e…

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Q: Question: Differentiate the following functions (1-cos2x' a) Y=| by chain rule. 1+cos2x) b)…

A: Product rule of differentiation:   Chain rule of differentiation:

Q: Given the first order IVP y'+3y : 3, 5a4e-3, 01 %3D with initial condition y(0) = 4. (1) Find the…

A: Consider the IVP,  y' + 3y = 5x4e-3x,      0 ≤ x < 1 y' + 3y = 5x 4e-3x ,      x ≥ 1  Initial…

Q: 29 - For what values of a and b is | S x+3a-b axt 26 3x-5 Continuows at every X?

A: g(x)=ax+2bx≤0x2+3a-b0<x≤23x-5x>2

Q: Q3. Let g(x) = 1-0.5 cos x, x = [0, 1]. a. Show that g has a unique fixed point. b. Find the number…

A: It is given that,  g(x) = 1-0.5 cos x,  x∈0, 1 (a) Show that g has a unique fixed point. (b) Find…

Q: 23 + 6x² – 32 1. lim 4 x3 + 5x² + 4x bw e 2. lim w>-00 4+ e 3w sin(6t) 3. lim 40 sin(11t)

A: Given that limit problem and we solve use L'hospital rule . If we apply limit and function is 0/0…

Q: 4. If f:1 → R is differentiable on I and g(y) = yn for ne N and ye R what is (gof)' by usin chain…

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Q: : / ain(tun3x)dx cos²3x tan( tan3x) dx Evaluate: A -in|sec(tan3x)| + c 3 B 3 -In|cos( tan3x)|+C O…

A: On solving this we will get

Q: 16. lim x2 cos(2nx) = 0 %3D

A: As per our guidelines we are supposed to answer only one question

Q: 0/0 form Evaluate the following limits using l’Hôpital’s Rule.

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: iox e dx solue with Residue nethod 2 - x + 2ix +1

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Q: 5. If f:1 → R is differentiable on I and f(x) 0 ,f'(x) ± 0 for x € l if g(y) =÷ , y# 0 what is…

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Q: 5x*e", 0S1 y(x) =

A: Given

Q: In( cosh(2x) + sinh(2x) ) + In( cosh(2x) - sinh(2x) ) = Select one: O zero O 2x O 2 O None O- 2x O 2…

A: Topic- hyperbolic function and log

Q: 1 25. lim (x,y)→(4,0) (x² – 16) cos (x – 4)² + y²

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Q: 2 In cosy y4 1 [1] limy-0

A: After simplifying the function the form is 0 by 0. So, apply L'Hopital's rule to find the limit.

Q: Question: Differentiate the following functions 4 1-cos2x a) Y= , by chain rule. 1+cos2x) b) Y=…

A: Using chain rule of derivatives,  fgx'=f'gxg'x Yx=1-cos2x1+cos2x4 ⇒Yx=2sin2x2cos2x4⇒Yx=tan8x

Q: 35. Eliminate the parameter t in the followin x = 9+4tant y = 4+4sect 36. Eliminate the parameter t…

A:

Q: Solve using Bisection Method f(x) = x2 cos(x) with xl = -4, xu = -3, es = 1%

A: In bisection method we find root of a function when we are given an interval in which the root lies…

Q: Lim Sx- 3 大ロ3 2メー5メ-3 /50it was す S4 2. the - sint cost Lcost 1 sint cost 14 Onot of the above

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Q: 1.( ) L(t sinh t) = -A) 2.( ) Let z1,, be complex, then Arg(z, +=,) = Ar 3.( ) Let "-y'+ 2r = In (t…

A: Note- Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: 4) Exercie S Hst 2x+iy be a complex mumber such thet (-s(37)#0Then Re (tent3z))|c equal to: Sin Bx…

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Q: SINEN GCX)= 4X- XE -4 -4 2 PROVE THAT GIVEN FORM X=9(x) SATISEIES TIHE conv E RGENCE CRITERIA FOR…

A: To find the root of the equation fx=0 by the fixed point iteration method, apply the following…

Q: 12:28 AM Fri Oct 23 77% T +: 0 the formul a, = lim f Cath) - fla) an m tan +o find 3 equation for…

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Q: 2n3+n² sin(n)+6 48. Calculate lim,,→0 312 cos(m10n 19: (Proof is not required)

A: Use the algebra of limits to find the limit of the given fraction, and use a concept that limit of…

Q: 2x? — х — 1 lim b) х--1 4 — 3x? — х x² + 3x +1 lim x→-1 2x? – 3x – 5 а) VE- 2 m³ – 8m + 1 lim lim -…

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Q: In( cosh(8x) - sinh(8x)) - In( cosh(9x) + sinh(9x) ) = Select one: O zero O 17x O None Ox O 8X O- 17…

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Q: (x²+y2 ) prove ne du + y ax -2 sin2u ( Euler's Rule) 5. If u = cot-1 that x ду x+y

A: We use the Euler's rule of partial differential in homogeneous function to solve this problem.

Q: (a) Find the charge Q(1) and current I(1) in the RC circuit if E(t) = Eo (a constant voltage…

A: The differential equation governing the RC circuit is: RQ' + Q/C = E0 We need to find the particular…

Q: (9) Lim t-3 sin(z² +4t +3) 1² -9 t'

A: As per bartleby guideline for more than one question asked only first is to be answered please…

Q: Assume that after  months, butterflies’ populace  in 1000 is calculated as:…

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Q: Fnd general solation:. Cosx x2

A: Given: y'+2xy=cosxx2

Q: 2 +3 Evaluate S4) (-2) (22+4)(- dx. Enter In(x) for In(x), abs(x) for |x|, and arctan(x) for…

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Q: A rancher wants to fence an area of 6 square kilometers in a rectangular field and then divide it in…

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Q: Within the interval (-5.14, 7.41), for what value of a does f(r) take on a minimum if f(x) = -6.6…

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Q: Vz²+7-3 11. lim,→3 I+3 12. lim,0 sin 3z cos 3z-cos z 13. lim,→0

A: As per our guidelines we are allowed to answer only three subparts of a question. Kindly repost the…

Q: sin 3y limy0 5y 05 O 3/5 00 03

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Q: X+ 0.4Inx 04. limx→+o X+ 3lnx 05. lim, „(e* – 1)cosx e' – 1)cos> COSX 'x→0

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Q: sinh (1+Inx)= Select one: ex-1 2xe O Zero e Inx 2 O None e?x² +1 2xe x² +1 O 1+ 2x

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Q: I. Elimination of Arbitrary Constants D Assignm Eliminate the arbitrary constants in each of the…

A: Y=mx+h/m – i) Here h is parameter and m is arbitrary constant We have to eliminate m Now…

Q: 2Lim S+1 5+s2 y4 3 Lim 3- yマyチマy4g ④ 文 Lim + Cos (4) メー→

A: In the given  question we have to find the limit of the…

Q: ← Z 3 Z (ancosno) z (ansinno) = z (z-a cose) Z-2axwoso ta azsing Z² 2ax cose + a²

A: Introduction: Z-transformed is significant transformation in mathematics. In many fields, it has…

Q: cos (T + h) + 1 41. lim h 0 1o dyhori of onil

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Q: 1) LtZ be a solukion (5) of complese mumber then the sinh Z+ Coah z -e is Z=1?

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Q: 1. y = x - x'cosx + 2xsinx + 2cosx 2sim x-1 2. y= cosx+2 3. tan(xy) + xy = 0 4. y= x 5. y = xArctanx…

A: The given function is y=xcosx. We know that duvdx=udvdx+vdudx.

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.