dx J (9x2-36)3 a. b. rV2-ezx dx ex V5+ln²x dx C.

Q: Solve the following: 1. Evaluate ſ x=dx 2. Evaluate S 4 dx 3. Evaluate S (x²+ x³)dx 4. Evaluate S Vx…

A: A detailed solution is given below

Q: alluse The g auss elemina fion to find the 2. -3 2. -2

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Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 4 1 lim t→+∞ \ 3t2 +4' 2t (?, ?)

A: The given limit ; limt→+∞t2+43t2+4,12t

Q: Evaluate the definite integral. Using Fundamental Theorems of Calculus. (x2 - х) dx х2 +x+ 1

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Q: Activity 1.5.3. A company manufactures rope, and the total cost of producing r feet of rope is C(r)…

A: Given problem :- A company manufactures rope, and the total cost of producing r feet of rope is C(r)…

Q: Consider the following functions. 3 f(x) = Vx - - 3 3 g(x) = x – 3 Sketch the region bounded by the…

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Q: -z“, where T is The temperature at a point (x, y, z) is given by T(x,y, z) = 200e measured in…

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Q: 2x f(x) 1< x < 3 to + 5 lim n → 00 i = 1

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Q: Evaluate the following limit: x + 2 lim x→-3¯ x² -+ 2x – 3 O +∞ 10

A: The given limit,        limx→3-x+2x2+2x-3

Q: Determine the extreme values of the function f(x) = 2 cos(x) –1 on the interval [0, 27].

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Q: integrate (2x + sqrt(x)) dx from 3 to - 6 A. 27 +2√3+4√6 B. 27 + 2√3 C. 27 - 2√3+ 4√6 D. 27-4√6

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Q: Solve the following integrals: 1. S 7e*dx 4. S 12*+1dx 5. S-dx 2. S(5ex – 6*)dx 3. Ј 3(5)dx 6.…

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Q: furt A)APproximate tue area unde hex)=X2 from x=0 to X=2u5ing four rectungles and X=0 a left and…

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Q: Answers a) A=7In(so)

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Q: -2x 3. lim, 0 sinx

A: This is a problem related to limit of the function. Based on the general formula and concepts we…

Q: (1-) 3 4. lim

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Q: 9.) A particle moves in a straight line according to the law of motion: s=cos(x). a. Find the…

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Q: 26. da (x² cos y+ sin 2y) =(ry) x(- sin y y') + (cos y)(2z) + cos 2y - 2y = x-y' +y·1 = %3D %3D dx…

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Q: Evaluate the iterated integral. T/4 '5 y cos(x) dy dx

A: A detailed solution is given below

Q: lim (t i - 6 j +1° k). -5 (t i – 6 j + r² k) = i i+

A: Topic:- limit and calculus

Q: A particle is moving in a straight line according to the position function s(t) = t³ – 6r² +9t + 5,…

A: Given: s(t)=t3-6t2+9t+5,t≥0 d)After breaking once the velocity of the particle becomes zero.i.e. v=0…

Q: 12 dx х3 — Зх2

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Q: 3. Find the area of the region inside the circler-3 sine and outside the limacon r= 2 - sine. Sketch…

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Q: Describe the graph of the equation. r = 3cos ti - 4 sin tj +k O An ellipse in the plane x = 1,…

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Q: Find the value of the derivative of g (x, y) when we restrict to the curve defined by x = cos t and…

A: Differrtiate with respect to t

Q: Evaluate the definite integral. Using Fundamental Theorems of Calculus. (x?2 - х) dx x2 + x +1

A: ∫01x2-xx2+x+1dxit is a improper fraction ( degree of Numerator= Degree of denominator)Using long…

Q: 2 - (2x 3y)dx - (2y + 3x)dy 0

A: 2)-(2x-3y) dx-(2y+3x) dy=0dydx=(2x-3y)-(2y+3x)dydx=3y-2x2y+3xdydx=3yx-22yx+3y=vxdydx=v+xdvdx

Q: What is the differential equation whose solution represents the family y = Ae3x + Be 3x+Ce4x? %3D O…

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Q: Evaluate the integral using the following values. x dx = 60 x dx = 6, dx = 2 J2 %3D 5x dx J2

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Q: Use a double integral to find the volume of the region under the graph of f(x, y) = xy and above the…

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Q: Find the general solution to the ollowing differential equations: (A) y = 2yx(y'+3)+13x %3D

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Q: Water is being poured at the rate of 2z m' /min into an inverted conical tank that is 12-meter deep…

A: We need to find rate of water leaking.

Q: What is the angle between the vectors u = and v = ? 213° O 188° O 111° 120°

A: Solution:

Q: х2 +7х — 3 (2х + 1) (х dx 2)² —

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Q: V 3 (d) r(1/6 + At) - r(n/6) = 3 COS At sin At cos At + SV3 sin At it

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Q: What are the dimensions of an open-top right circular cylindrical can that will hold a volume of 512…

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Q: 1. Find the derivative of the following. f(x)=13x* -7x²+5x²+11x+75 a.

A: Formulas:ddx(a f(x))=a ddxf(x)ddx(xn)=an xn-1ddx(a)=0;  where a is a…

Q: Evaluate the iterated integral. /4 y cos(x) dy dx 地

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Q: Matching Type. Match the functions in Column A with their corresponding antiderivatives in Column B.…

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Q: d d. Calculate ri(t) - r2(t)] and ri(t) x r2(t)] first by differentiating dt the product directly…

A: r1(t)=9t i +9t2 j+6t3 kdr1dt=9 i +18t j +18t2 kr2(t)=t4 kdr2dt=4t3 kr1(t)·dr2dt=(9t, 9t2, 6t3)·(0,…

Q: The motion of a point on the circumference of a rolling wheel of radius 3 feet is described by the…

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Q: 4.Graph one cycle of function given below. State domain, range, period, phase shift, vertical shift…

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Q: Find the first partial derivatives with respect to x,y and z f/x.y.2)= 3x'y- 9xyz 1 10 yz? 9xyz + 10…

A: Given:         fx,y,z=3x2y-9xyz+10yz2 First partial derivatives with respect to x,y,z.…

Q: Find the area of the surface generated by revolving the given curve about the y-axis. 8xy? = 2y6 +…

A: We need to find the surface integral.

Q: Preview Activity 1.5.1. One of the longest stretches of straight (and flat) road in North America…

A: We have to find the slope.

Q: Now, let's discuss the difference cases of solution to a given system of linear equations. There are…

A: Given problem :- Now, let's discuss the difference cases of solution to a given system of linear…

Q: QUESTION 10 If you have $51,000 in student loans at an interest rate of 3%, compounded monthly, what…

A: Solution:

Q: - 9y" = 27 %3D

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Q: Evaluate the improper iterated integral. x2 dy dx 1 + y?

A: The solution is given in the next step.

Q: 1 Given that 1 > x" with convergence in (-1, 1), find the power series for with center 1- 9x4 n=0 0.…

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