Evaluate: ³₂(4x²y — z³) dz dy dx

Q: Determine the values of r for which the given differential equation has solutions of the form y = t'…

A: To find for what  values of r the given term becomes solution of differential equation.

Q: Find the total area between the graph of the function f(x) = x + 1, graphed below, and the x-axis…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: True or False: Given a vector v, the vector -v will have an opposite magnitude. A True B False

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Q: - 3x17 +10+10 - ) 4x19-3 b) (4x2 - 1)(7x3 + x)] + 100

A: Note: As per our company guidelines we are supposed to answer first three sub-parts of the question.…

Q: VII. Given a region R enclosed by the curves y = 1 + sin (F), 4 as shown below. (2,4) (2, 2) (-2,0)…

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Q: Evaluate the integral: f/2 sin(4t-u) du dt

A: To evaluate: ∫π2π∫0tsin(4t-u) du dt

Q: 4. x-1 x² + 5x+8 Ja da

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Q: Evaluate the following limit, if it exists: lim x->7 = √x + 2 - 3 / x-7 (The square root covers…

A: In this question, we will evaluate the given limit expression.

Q: What is the direction of the vector with an initial point of (3,-5) and a terminal point of (8, 6)?…

A: The initial point is (3, -5) and the terminal point is (8, 6)

Q: 3. Determine whether the following pairs of functions are linearly dependent or linearly…

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Q: Whatis the equation of the line that passes through (-3,5) and is parallel to theline 4x - 2y + 2 =…

A: The line passing through -3,5 and parallel to the line 4x-2y+2=0

Q: ¡xr-¹e-λx, x>0, r,λ > 0. Given f(x) Γ(r) 1. Find f(x)dx.

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Q: II. Evaluate the following integrals. 4. J 9x - 5 dx 18x + 13 9x² 6

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Q: Find a number in [0, 1] such that the difference of one third the number from its cube is minimized.…

A: Let the number be x. Let f(x)= x³-x/3 So, f'(x)= 3x²-1/3

Q: Determine the values of r for which the differential equation y + 2y = 0 has solutions of the form y…

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Q: Evaluate the limit using L'Hôpital's Rule. 11x³ lim x-0 sin(x) = x (Use symbols and fractions where…

A: Givenlimx→ 011x3sinx-x

Q: 1 sinh x cosh3 x √9-cosh² x dx

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Q: 5. Evaluate : p.v x² -∞0 (x²+3)² 8 dx

A: Concept: Some important integration formulas: ∫1a2+x2=1atan-1xa+C Where C is constant Reduction…

Q: 2. S 2x 2 5+2x+x -dx

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Q: Evaluate the indefinite integral given below. Provide your answer below: f6e4 tan (2x) sec² (2x) dx…

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Q: Evaluate the limit: lim_ (x - ln x)* x→0+

A: Using L Hospitals rule , Value of given limit is evaluated.

Q: √2+x-√2-x X lim- --0

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Q: Does the following graph represent a function that satisfies the following conditions? f(0) = -2…

A: Here we need to cross check the given conditions are applicable to the graph of the function or not.…

Q: -3 (x² - y²)²] Evaluate: ₁²² x+y du dt

A: Given

Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (=) < 0. ƒ(x) has a root in [0,1]. If we…

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Q: 5x -3 2 Evaluate: f fx fdz dy dx 3x 2

A: As per our guideline we are allowed to answer only one question. Kindly repost the other question as…

Q: S √x²-25 dx X

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Q: Determine the values of r for which the differential equation ty"-5ty' + 5y = 0 has solutions of the…

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Q: IV. A small business determined that the price-demand and cost functions for producing and selling x…

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Q: Evaluate: ƒ³, ƒ²₁ √√₁²[z³(x + y)³] dz dy dx -3

A: Given :∫-33∫-12∫01z3x+y3dzdydx

Q: I. Evaluate the following limits. 1. lim sinh r → r r→0 sinhr – r

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Q: √ x-1 x² + 5x +8 dx

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find the area of the region bounded by the curves 1 y (x+4)²² y = 4 and the x-axis using vertical…

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Q: 2. Evaluate all of the integrals. b. 2|x - 21 dr

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Q: Suppose y=f(x) is a curve that always lies above the x-axis and never has a horizontal tangent,…

A: derivative

Q: ¹₁¹+x² x + 2y dy dx -12x²

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Q: R is the region bounded by the functions f(x) = - +3 an exact answer. Provide your answer below: A =…

A: The given two functions are:fx=-x23+4x3-103 and gx=x23-10x3+103We need to find the area bounded by…

Q: A particle is moving along a horizontal line such that its velocity in m/s is given by v(t) = 2t²…

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Q: Determine the derivative of the following function. Do not simplify.  y = (x - 2)3√2x-1 (sqaure…

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Q: Which of the following is true about the function a(x) = 21² +1-6 #-+-2 O A. a(z) has an infinite…

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Q: Flag question Evaluate: ³²₁ [2³(x + y)³] dz dy dx

A: Let's evaluate given triple integral.

Q: What is the equation of the tangent line to the curve y = at point (0, 0)? O none of the choices O y…

A: Given :      y = 3√x    Point : (0 ,0)

Q: x 4 dx (x²+4)² S

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Q: Find the value of the following definite integrals. Show your solution. 1. f(x¹+4) dx 2. (cos x +…

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Q: Determine the instantaneous rate of change of the function πt ³ √x sin 2 f(x) = LV x3 1 + √t at x=2.…

A: Leibnitz integral rule.

Q: Find the volume of the solid generated by revolving the region bounded by 2y = e-x², the x-axis and…

A: We have to find the volume of solid generated by revolving the region bounded by 2y = e-(x^2) , the…

Q: Question 8 Determinethe equation of the tangent line to the curve, y = 3x4-2x-1 4-x² , at x=1.

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Q: Evaluate the integral: S772 Sỗ sin(4t – u) du dt t/2

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Q: Determine the derivative of the following function. Do not simplify. y = ecosxsinx

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