Part 1 Find  PK + 1 for the Pk PK=1 + 6 + 11 +...+ [5(k-1)-4] + (5k-4)   Part 2 Prove the inequality for the given integer values of n. n!>2n, n≥4

Q: How many petals does the graph of the rose curve r=4sin(3θ) have? Enter your answer in the box

A: For the function, r=asinnθ    or    r=acosnθ If n is odd then there are n number of petals. If n is…

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Q: Question 4 Given that v = (0, -2) and w=(5, -8), what is w - v? A B C D (-5, -6) (-5, 6) (5,6)…

A: v =<0,-2> w = <5,-8> We have to find w-v

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Q: Evaluate the given definite integral. -23 125 th In x

A: let D=∫123lnxxdx

Q: 17) Use the Binomial Expansion Theorem to determine the coefficient of xº in the expansion of (x² +…

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Q: Taylor Power Series 5. Find the first 5 terms of the power series Σ (-1)^(n+1)(x-2)^ 222 'n=0

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Q: 5. Evaluate 3x 4e³x -dx 3x e³x +1 S-

A: given integration ∫ 4e3xe3x+1dx

Q: Question 8 What are the domain, range, and period of the function f(θ) = –3cos(–2θ)? Answer in…

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Q: _et f(x, y) = x+y+xy. Find f ₁² f(x, y)dxdy. Enter the exact numeric answer.)

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Q: Find the limit. lim (x,y) → (9, 9) 3 3,,2 (x²√³ - x³y²2) -

A: Apply L'hospital rule in limit

Q: If you want to earn 15% annual simple interest on an investment, how much should you pay for a note…

A: It is given that the annual simple interest on the investment is 15%.  also the amount after 3…

Q: Find the indicated partial derivative. V = In(r4 + s5 + tº); Ꭷ3v ərəsət Ꭷ3v ərasət

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Q: Find the equation of the tangent plane to z = e²+x+x³ + 10

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Q: -5x-2y 2x + y x 2z = -2) = 5 +z = 5 =

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Q: 5. The graph below shows the function h(x) over the interval 7≤x≤7. At which x-values is h(x)…

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Q: The cost of sending a large envelope via first-class mail is $0.76 for the first ounce and $0.18 for…

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Q: f(3) = lim f(x)= x-3 f(5) lim f(x)= x-5 lim f(x)= lim f(x)= x-3° lim f(x) = x-5 lim f(x)= 1-5 M lim…

A: When function continuous at x=1⇒limx→afx=faOR⇒limx→a-fx=limx→a+fx=fx

Q: Consider the following. ) = \, P(7, 1), u = i + j y 5 (a) Find the gradient of f. f(x, y) Vf(x, y) =…

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Q: e(4²)* + e* (4²*) (4)* + 4° dx

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Q: A circular swimming pool has a diameter of 12 m, the sides are 3 m high, and the depth of the water…

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Q: Suppose that lim an = 5 and lim bn = 9. n-0 n→∞ Determine the limits. lim (an + bn) = n→∞o lim a =…

A: We are given that limn→∞an=5 and limn→∞bn=9.We need to find the given limits.

Q: 4x² +28x + 25 (x + 7)(x + 2)² 1 x+7 B (x + 2) 3 (x + 2)²

A: NOTE: Refresh your page if you can't see any equations. . use the partial fraction…

Q: Find the critical points in the domain of the function f(x) = 9x³ – 8x. Enter the exact answers in…

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Q: What is the exact value of cos(495°)? A B C D 3 2 √2 2 이 이뤄

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Q: Consider the following differential equation to be solved by the method of undetermined coefficients…

A: According to question,Given differential equation,y''-2y'+10y=ex cos3x

Q: . Find the length of the segment indicated. Round to the nearest tenth if necessary. 49 7

A: To determine the value of x

Q: Find the value of c that makes the function continuous at x = 0. 8x - 4 sin 2x 7x³ C= f(x) = X #0 X…

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Q: Let C be the curve of intersection of the parabolic cylinder x2 = 2y, and the surface 3z = xy. Find…

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Q: Determine the value for c so that lim f(x) exists. X-5 f(x) = 1 5x+C, -x+10, for x>5 The value of c…

A: If limx→af( x ) exist then limx→a-f( x ) = limx→af( x ) = limx→a+f( x )

Q: = x³ and What is the volume of the 3D region, whose base is the region between the curves y = y = √,…

A: We have,   Curves :- y = x3 and y =  √x  Cross section are squares.

Q: h(x): x² - 7x + 10 x-5 a x 5 x=5 8. Let for some constant a. If h is continuous for all real…

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Q: A plane has parametric equations x = 2-s + 3t y = 4 + 3s-t z = -5 + 2t where s, t E R a) Find the…

A: Given equation  x=2-s+3t y=4+3s-t z=-5+2t

Q: Find the volume of the solid obtained by rotating the region bounded by the given graph about the…

A: We have, y=x2 , y= 2x, about the line x= -1

Q: What is the reference angle of θ if θ = –137°? A 43° B 47° C 137° D 223°

A: Explanation of the answer is as follows

Q: 2. For the vectors a = (1, 2, 3), b = (2, 1, 3), and c = (1, 1, 0), show that the following is true:…

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Q: What is fxe- dx ? -x Oxe xee+C Ox²e-2x 2 + C X -xe-* — e * +C x² e-x 2 + C

A: Consider,

Q: Subject: calculus  what is the definition of derivative?

A: Calculus

Q: The population of a city is modeled by the equation P(t) = 479,442e0.1t where t is measured in…

A: The population of a city is modeled  by the equation  P( t ) = 479442e0.1t Where t is measured in…

Q: Q5 Use the graphs below to fill in blank for Q(5.1)-Q(5.6). Write DNE" for Does Not Exist" or NEI"…

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Q: F(t )=100,000t for the next 9 years. What is the Present Value of this income stream over the 9…

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Q: - y=t? –t, t = 2x2+1, what's the dy dx for x=1?

A: We know that the derivative of x^n=nx^(n-1)

Q: What present value amounts to $358,312.09 if it is invested for 5 years at 16% compounded…

A: What present value amounts to $358,312.09 if it is invested for 5 years at 16% compounded…

Q: Decide from the graph whether a limit exists. If a limit exists, find its value lim F(x) x→-2

A: If the limit exist then the left hand limit and right hand limit are equal

Q: 10. for fx fx xy f₂ y f(x,y)=3x³y² + 4(3x+2y)³ find

A: The given function is;  f(x,y)=3x3y2+4(3x+2y)5 Find the fx, fxy, fy, fyx.

Q: r(t) = ti+t²j+ + 1 {/f²k 2

A: Solving the problem

Q: Find a formula for a cubic function f if f(3) = 24 and f(−1) = f(0) = f(4) = 0.

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Q: a. For the function and point below, find f'(a). b. Determine an equation of the line tangent to the…

A: f(x)=-9x2.

Q: The concentration of a certain medicine t hours after injection into the bloodstream is given by…

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Q: Find the equation of the plane determined by the intersecting lines: (x-2)/3=(y+5)/-2=(z+1)/4 and…

A: We have to find the equation of plane determined by the intersection lines.