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Q: V(PQ),V (PR), and V(PS) are 1. Find the volume of the parallelepiped PQRS if the vectors…

A: Solution of 1st question.

Q: Show that the differential form in the integral below is exact. Then evaluate the integral. (-2,4, -…

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Q: Part A) approximate the area under h(x)=x^2 from x=0 to x=2 using four rectangles and a left…

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Q: Describe the domain and range of the function. (x, y) = 9x2 - y Domain: y): x is any real number, y…

A: We need to find domain and range.

Q: denominator is a binomial.

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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: Determine the generating function of the following sequence {0, 0, 0, 1, 1, 1, ....}

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Q: Find the limit V1+t4 dt lim

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Q: esing pyphagoras th, Diff wt to t 2xda +rydy 20 at da dt az3 m

A: Apologies for the inconvenience.   Let, x = the distance from the wall. y = the height of the top of…

Q: Match the vector field with its graph. F(x, y) = yi y 1信 5 5 y 5 -6+ -5+

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Q: 5 4 3 1 T1/2 3π/2 -1 -2 -3 + -4 -5 The graph of the function f(x) = cot x is given above for the…

A: Solution is given below:

Q: Sol V= cotcex) dx /2

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Q: e. Write a couple of careful sentences that describe the behavior of the temper- ature of the potato…

A: The given table is: t 0 15 30 45 60 75 90 F(t) 70 180.5 251 296 324.5 342.8 354.5 We have to…

Q: Find the area between the loops of the limacon r= 7(1+2 cos 0). Area =

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Q: Evaluate the definite integral. Using Fundamental Theorems Calculus. sin x 4 – x² dx V1 + x2

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Q: d'y Find dx? 2 y = (2а-3)? dy 48 dx? (2г - 3)" O dy -12 da? (2г- 3)" O d'y 12 dx? (2a-3) dy -8 da?…

A: y=2(2x-3)2

Q: 20) Solve the higher order initial-value problem y"=x+1/x;y(2) =1 and y '(2) = 0 1 7 7 1 15 + -- X-…

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Q: Verify Green's Theorem by evaluating both integrals dA Əx ay, or the given path. C: boundary of the…

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Q: ||r'(t) × r"(t)|| ||r(t)||* Use the formula k(t) to find k(t). r(t) = e10ti + e-*j K(t) =

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Q: 1 T/2 3t/2 -1 - -2 + -3 + -4 - -5 The graph of the function f(x) = sec x is given above for the…

A: Topic:- function and calculus

Q: What is the annual nominal rate compounded daily for a bond that has an annual yield of 5.2%? The…

A: Use formula of annual percentage yield

Q: Verify Green's Theorem by evaluating both integrals ƏN dA y? dx + x² dy = ay for the given path. C:…

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Q: Evaluate the definite integral. NOTE: Enter the exact answer. ti + tj dt

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Q: 10 10 If f(x) dx = 19 and f(x) dx = 6, find the following. %3D f(x) dx

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Q: Determine

A: Given,             limx→1x2-4x+3x2-x

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

A: Solution:

Q: E1 Fnd all of the Porst order partial derivatives Toll wing fanctions. a)そ= x+5y x Sin (y). b) fexy,…

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Q: (b) Solve the following initial value problem: dy cos? t sin t y(0) = 2. dt

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Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by…

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Q: The graph of f'. 2+ 1- (2,0) -3 4 -3 ±1+ -2+ (-2,-3) (2,-3) 5. The graph of f', the derivative of f…

A: We have to find the value of f(5).

Q: Evaluate the following: 1. S(x3+ 3x?)dx

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

A: Topic:- limit and calculus

Q: QUESTION 4 At an awards ceremony, 6 women and 4 men are each to receive an award and are to be…

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

A: Solution:

Q: 14) Find aset of parametnic equetians for the rectangular aquetiag d= 4x2 tust Setisfies fue…

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Q: (x – 2)y' + y = e“, y(3) = e³ +1

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Q: Describe the graph of the equation: r = 7hi – 9j + (1 + 61)k. [Choose the correct answer.] O The…

A: Given problem:- Describe the graph of the equation: r = 7ti − 9j + (1 + 6t)k.

Q: 1. Find the volume of the parallelepiped PQRS if the vectors V(PQ),v(PR), and v(PS) respectively 31…

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Q: Use the figures to evaluate the function if f(x) = sin x. (x,1) f(a + B)

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Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

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Q: Find the arc length of the graph of r(t) = = ev2'i + e¬V2'j+ 2tk, 0<t < v2 ln 7 NOTE: Enter 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: In(2+x) lim, x+-1 X+1

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Q: Evaluate the double integral over the rectangular region 9(a sin(y) – y sin(x)) dA; R= {(x,y) : 0…

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Q: 13. Solve the following system of equations using either the substitution method or the graphing…

A: Linear equation: Linear equations are first-order equations. An equation with a homogeneous variable…

Q: Use the limit definition to find the derivative of f (x), this means no short cut rules, f(x) = x? –…

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Q: Consider the following. f(x) x(x2 – 11x + 35) - g(x) = x²

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Q: Find the exact arc length of the curve x = + 2) ? from y = 1 to y = 5. Enter the exact answer. L =

A: Given problem:-

Q: A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 550…

A: We have to find the minimum cost.

Q: 12 dx х3 — Зх2

A: