1- On donne: a- Résoudre l'équation: f(x) = 0 b- Trouver la dérivée : f'(x) c- Calculer: f(In 2) 1- Given : f(x)= e²x - 3e* (x ER) a- Solve the equation: f(x) = 0 b- Find the derivative : f'(x) c- Calculate: f(In 2)

Q: Evaluate. 34) f' x(x2 + 1)4, 0 dx

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Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. [e³ 34x dx =…

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Q: 3. The differential equation dy = =X dx 1. will produce a family of quadratic functions. II. will…

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Q: Suppose (2, -1) is a critical point of a function f with the continuous second derivatives. If fxx…

A: We need to choose correct option.

Q: Evaluate the integral given below. Check your answer by differentiating. NOTE: Enter the exact…

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Q: c) [ : Consider the series: 1 49 7-1+ 1 + i) Is the given series a geometric series? Explain. ii)…

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Q: Q1 (2 Let R be the region bounded by y = 0, y = x², x = 1. a) Sketch the region R. b) Evaluate the…

A: Here, the region of integration is: y=0, y=x2,x=1

Q: 7. Find the exact length of the curve: x (t) = 2t, y(t) = 2t, 0 ≤ t ≤ 1

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Q: 1. Integrate using an appropriate method. [2si 2 sin³(r) cos² (r)dr

A: The given integral is: I=∫2sin3xcos2xdx   As we know that; The trigonometric identity; sin2x+cos2x=1…

Q: Let f(x, y) = 6 - x² + 2y²-5x - y. The point (,) is a saddle point of the function Select one: O…

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Q: 6. Find an equation of the tangent line to the curve at the indicated point: (t) = t cos(t), y(t) =…

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Q: Find the average value of the function 1 2x + 5 on [1,4]. f(x) =

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Q: Question 5 (a) Find an equation of the curve that passes through the point (0, -2) and whose slope…

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Q: Model the data using an exponential function f(x) = Abx. f(x) = X f(x) 0 1 128 64 2 32

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Q: 1) 3 Use reduction of order method with y₁(x) = e³x to find a second solution y2 for the DE: y" - 9y…

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Q: 9. Evaluate (2+2 +31 +3) dr by interpreting it in terms of areas.

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Q: The Integral fi fig(z,y) dyda can be written as: 21-9(x,y) dzdy Select one: O True O False

A: We can solve this as follows:

Q: Which of the following is not an improper? A B D Sªcot (x) dx © Sese(x C E S'tan (2) de dx csc (x)…

A: We know that an integral is called improper if one or both of the limits of integration are infinity…

Q: Evaluate the integral and check your answer by differentiating. x² +8x4 1 x6 1² dx +C

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Q: Find the gradient vector of the function f(x,y) =. Select one: O None of the others. - O O + 6xy,…

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Q: Given the triangle not drawn to scale A = 16/ A 25 13 , find the measure of angle A using the Law of…

A: We can find the angle A using cosine rule as below.

Q: Choose the gradient of the function \(f\) defined by f(x y) √1 (4x 5y)². O None of the others 4x+5y…

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Q: f _____________, then the graph of the polynomial function is symmetric about the origin. A.f(x) =…

A: Note that, a function that is symmetrical with respect to the origin  is called an odd function.

Q: What is the value of the integral Select one: O 64 O 16 O None of these O 32 08 CO 2rydydz?

A: Given:       ∫04∫x42xy dy dx      =∫04∫x42xy dy dx     Taking out constant        =∫042x∫x4ydydx…

Q: The minimum value of the function f(x, y) = x + y subject to constraint x² + y² = 2 is not equal to…

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Q: The function z = Select one: O True O False f(x, y) has a local maximum at the critical point (3,-1)…

A: Given z=f(x,y) D(3,-1)=4 and fxx(3,-1)=-5

Q: 9. Find if x (t) = t + sin(t), and y(t) = t - cos(t). doe

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Q: Use the double integration find the area of the parallelogram whose vertices are A(1,0), B(3,1),…

A: Area of parallelogram

Q: 2. If y is the solution of the initial value problem = 3(y - 1)(y-2) with y(1) = 3, what is lim…

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Q: Determine whether yp₂(x) = x is a particular solution of the following DE or not. y" + 4y = 4x.

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Q: 8. Graph the curve and find the area that it enclosed: r = 2 cos(0).

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Q: 2. Integrate using an appropriate method. 1 PVR-36° dr

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Q: 1. Find the critical points of the function f(x, y) = x² + 4xy. 2. Find the local maximum and…

A: Note: As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Compute /16-³ dac

A: Solution of given question is written in below steps.

Q: Given than [ f(x) dx = 4 and the following is NOT TRUE A B C [ f(x) dx = 8, which of [2f (a) dx = 24…

A: We know, ∫abf(x)dx=-∫baf(x)dx

Q: c²e-2x³ dx [ +C

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Q: Q2. Consider the function f: f(x, y) = x² - 4x + y² − 6y ] Find all critical points of f. Find the…

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Q: Find linearly independent functions that are annihilated by the given differential operator. (Give…

A: The characteristics equation is (m-3)(4m+5)=0. So,                   m-34m+5=0⇒m-3=0  or…

Q: 1. Solve the differential equation: ² doc + 2xy = Inx, y (1) = 2

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Q: The integral ſº, ſº₁ x – y dædy is equal to: Select one: 0 O2 O 4 O None of them O-2

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Q: b) [.. Determine whether the series Σnºen-7 n=1 is convergent or divergent.

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Q: Choose the area of the region enclosed by: x = 0, y = 0, y = -x + 1. Select one: y-1 LL" dady O None…

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Q: 2) A) (::.. y" + 9y = 0 B) i y" + 9y = 0, y(0) = 0, or else show that it has no solution ... )…

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Q: Use Definition 7.1.1, DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t > 0. Then…

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Q: A farmer is building a fence to enclose a rectangular area consisting of two separate regions. The…

A: Given problem:- A farmer is building a fence to enclose a rectangular area consisting of two…

Q: Evaluate the integral and check your answer by differentiating. NOTE: Enter the exact answer. 3 S[ ²…

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Q: The total cost (in dollars) of manufacturing x auto body frames is C(x) = 60,000 + 800x. (A) Find…

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Q: 9. Find a formula for the general term an of the sequence: {1,0,1,0,1,0,1,0,...}

A: Given sequence is  { 1,0,-1,0,1,0,-1,0,....} Now we give formula of this sequence

Q: n 1 ² Σ (sec (2 + ²) - 2 (2 + ² +)) - nxn i=1 3. Express lim as a definite integral, f(a)da.

A: This is a integration problem

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. x³ (3x4 + 2)³…

A: We need to integrate ∫x33x4+23dxSubstitute 3x4+2=tDifferentiate w.r.t t12x3dx=dtNow∫112t3dt ---{1}