QY/ Find the direction devivative of f(x,y) = x₁² + yet at the paint (2,1), by the dirction of V = i-j

Q: 6 Find the area enclosed by the given curves. * y = x³ and y = 4x

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: f(x) = 3x² - 5x+21

A: SOLUTION-

Q: Find F(s). ℒ{t3e−4t}

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Q: Find the derivative of the function f(x) = = sin(x) - 1 cos(2x) + 1 4

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Q: 2 S-2 2 S+2 Option 3 Option 2 O *The Laplace transform of the x(t) is 2e21 1 S - 1 s²+1 Option 1 O…

A: Let's do laplace transform of given function.

Q: 2 X 2 - a² dx X

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Q: Find f'(x) where f(x) = esina Of(a)=esing cos O f'(x) = sinx. ecosx ○ f'(x) = ecos sinx . O f (2) =…

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Q: Let V be the volume of the solid obtained by rotating the region above the x-axis and below the…

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Q: c) L-1, 4s² - 21s+ 30 (s² - 6s+13) (s – 4) -

A: Above question is solved.

Q: Differentiate f(x) = a4x4 -3ax² with respect to x. Assume that a is a constant. f'(x) =

A: f(x)=ax4-3ax2 differentiate with respect to x

Q: Compute the following limit. 1-cos(z) as x approaches 0

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Q: Use the Laplace transform to solve the given initial-value problem. y'' − 4y' + 4y = t,    y(0) =…

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Q: What is the z-transform of the ?signal x(n)=(0.5)nu(n) Roc |Z| 0.5 Option 1 1 (1-0.5z-¹) 1…

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Q: * The z-transform of a signal is given below,its final value Z-1 2-¹ (1-2-4) x(z) = 0.25 (1-z-¹)²…

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Q: P1: Calculate the area bounded by the curves: A. y = x² and y² = x.

A: Since you have posted multiple questions which are not interlinked i can do first question(area-A)as…

Q: (x2+1) з xp x 0

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Q: Instructions 1. Write your complete solution for each item. It should be handwritten. 2. Make sure…

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Q: he polar equation for circle x^2+(y- 3)^2 =9

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Q: e²x 9e2 + 18e + 10 (d) / 5 dx

A: To evaluate: ∫e2x9e2x+18ex+10dx Substitute ex=u⇒exdx=du:…

Q: For the function whose graph is shown below, at which value of x is the graph continuous and…

A: We know  Function differentiable if it is continuous through out its domain   At sharp/corner points…

Q: f arctan y dy 3 ¥

A: Given problem:- ∫arctan(y)/y3 dy

Q: 1 S dx = 3x+2 0-²(3x + 2) + C O 2√3x +2+c 3 O²(3x + 2)² + C A O√3x + 2 + c

A: The given integral is: I=∫13x+2dx  ...1   As we know the Power Rule: ∫xndx=xn+1n+1+C ; n≠-1

Q: Let R be the region enclosed by the curves y = x³ and y = 2x². The area of R using vertical element…

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Q: Solve the following Differential Equations with Laplace Transforms y" - 6y + 15y = 2 sin (3t), y (0)…

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Q: Use the graph to determine the limit. (If an answer does not exist, enter DNE.) y c=-2 -3 + (-2, 3).…

A: The graph of the function is  To evaluate: a limx→c+fx, c = -2b limx→c-fx, c = -2c limx→cfx, c = -2

Q: (2x-1)dx 2x³-x²-27x + 30

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Q: Show that the interval [a,b] is complete

A: Given

Q: () without a calculator. We will do the followings: (1)- 1.2.3.4 7.6.5.4 1.2.3.4 I will introduce a…

A: Using definition of combination

Q: Question 4 (a) Solve the following: 4x¹dx (b) Explain with the aid of a sketch how this value can be…

A: we have to find the value of integral ∫-22 4x4  dx

Q: en the following total revenue (TR) and total cost (TC) functions for a firm, TR = 5820Q +4Q² − 2Q³…

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Q: along the line AM WI a magnitude of midpoint of the vertical side OB of the parallelepipe Express F…

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Q: 4. xy²1₁ X=1, x = 4, y = 0; about the x-axis

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Q: Find the constant a such that the function is continuous on the entire real line. f(x) = √5x², x ≥ 1…

A: We need to find a.

Q: g(x)=x5bx³ +a+c. Use calculus to: St (a) Find the critical points of g(x). (Round the y-value to 3…

A: Given a=15, b=12 & c= 15

Q: (b) [x² x²9x8 – 12x4 + 4 dx 2

A: We need to solve integral.

Q: 1 Suppose that I is a location function of an object, given as L(t) = We will compute the 3t - 7…

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Q: Find dy dx In y = e sinx O dy dx O dy dx O dy dx O dy dx = yey sin x =yey cos x = 4 1- ye cos x yey…

A: We can find the answer as below.

Q: f(t) to f' (t) Option 2 O F (s) to f(t) * Laplace Transform transforms a function from f(t) to F (s)…

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Q: 2. A certain plutonium isotope decays at a rate proportional to the amount present. Approximately…

A: Let  at time t the amount of plutonium is  A(t)

Q: 8 1 ₁ }(s) = = nº n=1 Show that finding the value of the Reiman Zeta for (2) is just the value Basel…

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Q: State the order of the given ordinary differential equation. (1-x)y" - 4xy' + 7y = cos x Determine…

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Q: f(secx tan² x) dx

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Q: 5. Find the vector equation of the line passing through A(4, -3) that is perpendicular to x - 3y + 6…

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Q: 3) Find the intervals where the function is increasing and where it is decreasing. f(x) = x² - 6x²…

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Q: Q1) L-1 a) cosht -1 b) 1 - cosht c) (cosh2t - 1) d)/(1-cosh2t) Q2) The general solution of y"" + 2y"…

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Q: differentiate the funtion y = cosh x - sinh x / cosh x + sinh x

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Q: Consider the following. y = = In(x²) Find y'. y' = Find the slope m of the tangent line to the graph…

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Q: Find the area of the surface generated when the given arc is revolved about the y-axis ㄷ y = 4 - x²…

A: We have to find area of the surface .

Q: Let F(x) = f(f(x)) and G(x) = (F(x))². You also know that f(9) = 7, f(7) = 3, f'(7) = 8, f'(9) =…

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Q: The function f(x) 2x³ + 42x² = one local minimum and one local maximum. This function has a local…

A: You must have an idea how to use derivatives to find the local maximum and minimum using critical…