Find the divergence of the vector field F = < y2², 22³, zy³ >. div F

Q: A thermometer inside a room reads 22°C. The thermometer is relocated outside the room. After one…

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Q: Question 2 Given the IVP: y" - 5y + 6y = 80, y(0) = 0, A) Use the Laplace transform to find Y(s). B)…

A: To solve IVP.

Q: el-3x = 4

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Q: ber of al real s) ber of qual/unique root(s) ber of ginary roots ber of s the graph ses the x- ber…

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Q: Find the indicated sum. 5 Σk(k+1) 5 k = 1 k=1 k(k+ 1) = (Simplify your answer.)

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Q: se the given zero to find the remaining zeros of the function. f(x) = x³ - 7x² + 4x-28; zero: - 2i…

A: Topic:- application of algebra

Q: 5. Find the value(s) of x where the tangent line is horizontal for f(x) = 3x³ - 2x² - 9.

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Q: Given f(x) = 2x+4 and g(x)= 3x² - 2x, find f(g(x)).

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Q: Question 3 A) Solve the given differential equation by variation of parameters: 2y" + y = 8x. B)…

A: (A) The differential equation is given as , 2y''+y'=8x Find the solution.

Q: fy(x, y) = llowing Find the partial derivatives. fx(x, y) = f(x, y) = 2y sin(xy) 75 Find the…

A: Given f(x,y)=2ysin(xy)

Q: 1. Evaluate ³132² - 12| dr. 2. Given F(x) = sinh 3r 2 √3+t dt. Find F'(0).

A: as per company guidelines  we can solve only first question  when multiple questions being posted.

Q: Write Sk- 1.8+2 9+3.10+ Write SK+1- 1.8+2 9+3 10++ (Type your answer in factored form.) Type your…

A: We have to find the term Sk and Sk+1.

Q: Find the complex zeros of the following polynomial function. Write f in factored form. f(x)= x³13x²…

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Q: W 3/4 i es 1 Find the area of the shaded region. Enter your answer as a reduced fraction. 0.5 0 05…

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Q: Using the Integral Test, the following series is convergent. Select one: O True O False n=3n²+5

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Q: Evaluate the integral 9 3 dx x(In x)5 || 9 3 dx x( In x)5

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Q: Evaluate the following three limits: i. lim x→1 ii. lim x-0 3@ iii. lim 2-e3a x-0 I

A: Given problems:- (i) limx→1ex-1-x3x2 (ii) limx→0e-3x-e-4x-xx2 (iii) limx→02x-e3xx

Q: rue or false. he integral True False f(a)de gives the area of the shaded portion shown. 3 -1 y =…

A: Given query is to find the statment is true or false.

Q: 1 For f(x) = 4x and g(x)= x, find (fog)(x) and (gof)(x). Then determine whether (fog)(x) = (gof)(x).

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Q: Estimate the area under the graph of f(x) rectangles and right endpoints. Rn = = Repeat the…

A: Area under the curve is given by= ∫161x+4dx we have given n=10

Q: 6. Find f(x) for f(x)= 2X-7 3x-2

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Q: Let the position of a swinging pendulum in simple harmonic motion be given by s(t) = cos(t) + sin(t)…

A: Given:- st=cost+sint

Q: Round your answer to the nearest integer. Compute the average value of the function f(x)=x²-3 on the…

A: As we know that, The expression for the average value of the function fx on the interval a,b is:…

Q: Consider the function f(x) = 3x · h(x) where h (2) = 4 and h' (2) = -3. Fill in each blank: Then…

A: We know that equation of tangent line at any point is given as - ( y - y1 ) = m.( x - x1 )   Here m…

Q: Consider the function f(t) = 5 sec²(t) — 9t³. Let F(t) be the antiderivative of f(t) with F(0) = 0.…

A: Given f( t ) = 5sec2t - 9t3F( 0 ) = 0

Q: Find the area between the curve y = x3 - 6x2 + 8x and the x-axis. Answer: 8 sq. units

A: Given y = x3 - 6x2 + 8x

Q: Find the complex zeros of the following polynomial function. Write f in factored form. f(x)=x4 +…

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Q: Find the derivative of y with respect to x if y= In (8x) S sin (7et) dt.

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Q: sinh 3r 2. Given F(x) = f 2 √3+ t dt. Find F'(0)

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Q: - 1 Find ²¹ dz x² +C

A: As we know that, The Sum rule: ∫fx±gxdx=∫fxdx±∫gxdx The Power rule: ∫xndx=xn+1n+1+C ; n≠-1 And use…

Q: Consider the function f(x) whose second derivative is f''(x) = 7x + 7 sin(x). If f(0) = 4 and ƒ'(0)…

A: Given: f''(x)=7x+7sin(x), f(0)=4 and f'(0)=3

Q: Consider the following table, and assume that f(x) and g(x) are differentiable functions with values…

A: Let's find value of h'(4).

Q: = f(x + Find +6)(x − 2)dx + C

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Q: Given 11 1(² f(x) dx = 3 and 10 f(x) dx = -3, find 10 f(x)dx.

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Q: Which of the following statement is true for the alternating series below? 8 Σ(-1). n=0 n5+1 The…

A: Solution: Given data, ∑n=0∞(-1)n 1n5+1

Q: Number of equal real root(s) Number of unequal/unique real root(s) Number of imaginary roots Number…

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Q: If F(x)= S.. 2 F'(x) = tan(t) dt, compute F'(x).

A: Find F'(x) where F(x) is an integral of t

Q: Given the pattern -36, 12, -4,... (a) Write an explicit formula for the pattern. (b) Write a…

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Q: Describe the sequence of transformations that are required to graph g(x) = -2(x-5)7+12 based on…

A: We have to find the sequence of transformations required.

Q: Obtain the general solution. (HOMOGENOUS EQUATION) 3. ydx + (2x - y)dy = 0

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Q: For f(x) = *(r² - 5t + 7) dt, compute ƒ'(x). 0 X

A: given function f(x) = ∫0xt2-5t+7dt          then we have to find f'(x)now ,f(x) =…

Q: What are the maximum and minimum values of f(x) = x + 2 cos x on the [0, π] interval

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Q: What can you say is true if f" > 0 ? Select all answers that apply. O f' is positive O f' is…

A: we need to write down the correct options.

Q: Consider the function f(x) 9x³ 2x² + 10x - 3. 3 An antiderivative of ƒ(x) is F(x) = Axª + Bx³ + Cx²…

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Q: Obtain the particular solution. (HOMOGENOUS EQUATION) 4. xydx + 2(x² + 2y²)dy = 0, when x = 0 and y…

A: Given differential equation xydx + 2( x2 + 2y2 )dy = 0

Q: A company's revenue for selling x (thousand) items is given by R(x)= Find the value of x that…

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Q: If T(t) represents the temperature of a cup of coffee (in degrees Celsius) at t minutes after 8…

A: Solution: Given data, T(t) = temperature of Cup of coffee in degrees Celsius.

Q: V= 2 attempts left Compute the volume of the solid formed by revolving the region bounded by y = 11,…

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Q: find the domain of composite functions, using additiona, subtraction, multiplication, and division.…

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Q: 3 f(x) = ², g(x) = x+1 H

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