Find f. f(t) =|| f"(t) - 3et+ 5 sin t, f(0) = 0, f(T) = 0

Q: A function f(x) is said to have a removable discontinuity at x = a if: 1. f is either not defined or…

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Q: Verify Green's Theorem by evaluating both integrals (ON-OM) d [[ y² dx + x² dy = √ √ ( ³x for the…

A: In this question, we want to verify the green's Theorem for the given integral.

Q: Find an equation of the tangent plane to the surface g(x, y)=x²-y² at the point (7, 4, 33). O…

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Q: USE NEWTON-RAPHSON'S METHOD IN FINDING ROOTS f(x) = ex²-2 + √√x + 2-3

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Q: At the beginning of an experiment, a scientist has 160 grams of radioactive goo. After 90 minutes,…

A: topic- exponential function

Q: The position of a particle moving in a straight line is given by s(t) = e-*cos(5t) for > 0, where…

A: We have to find the necessary equation that must be satisfied.

Q: Examine the function for relative extrema. f(x, y) = 2x² + 7y² - 4x − 14y + 12 (x, y, z) = ((No…

A: Given function: fx, y=2x2+7y2-4x-14y+12

Q: 6. Evaluate the following real integrals by residue theorem 3 T 211 I- -S do coso + 2 sing +3 ans o…

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Q: Determine whether the vector field is conservative. F(x, y) = (7y - x²)i + (7x + y)j conservative…

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Q: Given that calculate f'(-1). f(x) h(-1) h'(-1) = || || x¹¹h(x) 3 6,

A: Given, f(x)=x11h(x)h(-1)=3h'(-1)=6

Q: Consider the following second-order differential equation. 3y" + 2y' + y = 0 Find all the roots of…

A: We have to find the general solution.

Q: What is the maximum value of the function h(x) = 10x =—= 22² x² on the interval 0≤x≤ 40 and for what…

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Q: 3X y 2y = 4y + 8y = 2³x + 8x² 2X <-2X Ans: y = ₁2x + ₂xe + cze -25 X -3X 2 —=== ² + x + x + 1²/2

A: This is a problem related to ODE. Based on the general formula and concept we will answer.

Q: Determine whether the given set of functions is linearly independent on the interval (-00, 00).…

A: Given: f1x=2+x, f2x=x, f3x=x2

Q: Write an equation for the function graphed below. The y intercept is at (0,-0.2) -7 -6 -5 -4 -p 2 y…

A: To find the equation for the function.

Q: Find the centroid (x, y) of the triangle with vertices at (0, 0), (10, 0), and (0, 2). 18 15 X=

A: Consider a triangle with vertices at (0,0),(10,0) and (0,2)

Q: Question 17 V -2 8- 7 16 16 6 5- 4 3 رها را 2 1 -4 -7 1 > V V 2 3 4 5 Find an equation for the graph…

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Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

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Q: Consider the following second-order differential equation. 2y" + y = 0 Find all the roots of the…

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Q: S D

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: the function. x+1 f(x)= (a) Find the Inverse function of f. 1-¹(x) = (b) Use a graphing utility to…

A: Please see the below picture for detailed solution.

Q: Use the Factor Theorem to determine whether x+3 is a factor of P(x) = 2x³ + 6x²-x-4 Specifically,…

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Q: Find F as a function of x and evaluate it at x = 2, x = 6 and x = 9. = $₁² F(x) = F(2) = F(6) = F(9)…

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Q: | (8z + 4z³ - 6z²) dz? O 16z²+z4-2z³ + C O4z²+z4-22³ + C 16z²+z4+ 2z³ + C O 42² +224 + 2z³ + C

A: Solution: ∫8z+4z3-6z2dzApply the sum rule=∫8zdz +∫4z3dz -∫6z2dz

Q: The following table shows worldwide sales of a certain type of cell phone and their average selling…

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Q: I'm not sure how ti find the position vector. Could you please give me some instructions? Thank you.

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Q: I'm still confused on the position vector. The question is Let r(t) be the position vector…

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Q: Find a unit normal vector to the surface at the given point. [Hint: Normalize the gradient vector…

A: The given surface is zex^2-y^2-1=0 and point (6,6,1).

Q: elax upx dx

A: ∫1xlnx23dx

Q: Solve the differential equation by variation of parameters. y" + 2y' + y = e-t In(t) y(t) =

A: The DE is given as , y''+2y'+y=e-tlnt find the solution by variation of parameters.

Q: 000 is budgeted for production of the product, determine how that amo ion will be maximized when…

A: We are asked to find the maximize the profit

Q: Examine the function f(x, y) = x³-9xy+y³ +8 for relative extrema and saddle points.

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Q: dw = t³ and y = 7. Find dt Let w = cos(8x - 10y), where x =

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Q: -10 -10 10 (c) Describe the relationship between the graphs. The graphs off and f" are reflections…

A: Let's solve for c part.

Q: Find the area bounded by the given curves. Use vertical strip x² = y - 1 and x = y - 3

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Q: Find the determinant. x² -Ed 2x 5x4 W(x5, x²) = = (x²)(5x4) - (2x)(x5) The Wronskian ---Select---…

A: We need to fill in the blanks.

Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

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Q: Consider the following. [[X] = Sketch the graph of the function. Use a graphing utility to verify…

A: Here we have to sketch the graph and then finds its domain and range.

Q: ƒ(x) = (x³ – 4x) 10

A: Solve the derivative

Q: 3. (2xy-x + 2y - 1) dx +(4x²y² - x² + 4xy² -x) dy = 0

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Q: A proton traveling at 34.2° with respect to the direction of a magnetic field of strength 2.27 mT…

A: Given  θ=34.2° B=2.27mT F=9.44×10-17 N

Q: Prove the identity. cos(3x) − cos^3 x = − cos x sin^2 x − sin x sin(2x)

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Q: Evaluate the iterated integral. •π/2 [y/6 [5/y } 0 sin y dz dx dy

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Q: Sketch the image S in the uv-plane of the region R in the xy-plane using the given transformations.…

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Q: Determine whether the given set of functions is linearly independent on the interval (-∞0,00). f₁(x)…

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Q: Question 1 Find the total differential of the function z = 7x³y8 Odz = 7x¹y³dx + 7x³y+dy dz =…

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Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

A: This question can be solved using the concept of differential equation.

Q: Suppose 150 trout are seeded into a lake. Absent constraint, their population will grow by 35% a…

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Q: What is ette-t At- ○ - In [e* O ○ ○ dx e* + C] In [e* + e* + C In [e* e*] + C -In [ee] + C

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