Find the values of a and b that make f continuous every ²-4 If x < 2 f(x) = If 2 ≤ x <3 ax² - bx + 3 4x = a + b if x ≥ 3 B I b=

Q: Use part one of the fundamental theorem of calculus to find the derivative of the function. g(x) =…

A: Solution: The objective is to find the derivative of the given function

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Q: 2 Sketch the graph of each function for 0≤x≤27. a y=-sin x by=-2 sinx c y=-3 sinx d Explain to a…

A: 2. a.)  The graph of y = - sinx  is

Q: • show that (x, y, z) = PDE : 2²4 ахг 824 дуг + 2 x² + y² + z² = 0 8²4 dz² satisfies the

A: This question can be solved using the concept of partial differentiation.

Q: Solve the initial value problems dy 19. (x + 1)- dx -2(x² + x)y=x+1' x>-1, y(0) = 5 dy 17. 0 + y =…

A: Given (x+1)dydx-2(x2+x)y=ex2x+1       y(0)=5, x&gt;-1To find Solution of Differential Equation:

Q: 1. y=x² - 6x² +9x-3 2. y=2+12x-x³ 3.y=r°−2x +8r*

A: Note: According to our expert guidelines only first three subparts are to be answered kindly repost…

Q: F(x, y) = 6xyi + 3y²j is a conservative vector field.

A: Given :F(x,y)=6xyi+3y2j

Q: Short Answer 11. Calculate X+W for X- 3) 2 and W- or explain why this operation

A: Given X=70-1423 and W=-4111-122To Find:  X+W

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Q: hat are all of the solutions for the equation 3cos(3θ) – 8 = –11 on the interval of [0°, 360°)?…

A: NOTE: Refresh your page if you can't see any equations. .

Q: 6 By separation of variables, Solve the following 5 PDES :- учи ²4 dx2 0 o u(e,t) = u(5,t) =6 u(x,0)…

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Q: Consider the sequence 20, 14, 8, 2, ……, (a)    Write a recursive formula of the sequence. (b)…

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Q: show that V(x, y) = x 'f (2x+y) is the general Solution of av X du 2X 1 = V ду dax

A: Explanation of the answer is as follows

Q: A. Consider a 100-meter track used for foot races. The time it takes for a ru run the track can be…

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Q: Find the volume of the region bounded above by the elliptical paraboloid z=8-3x²-4y² and below by…

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Q: A solid is formed in the first octant bounded by the plane z = 6 - x - y and the cylinder 4 - x².…

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Q: For each of the following ,find fx fy fxx fyy fxx and fxy 1.f(x, y) = x cos+ ye*. 2.f(x,y) = y²x¹ey.…

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Q: 2. . If f(x) dx = 4 and 3g(x) dx = -9, evaluate [² [3f(x) + g(x)] dx

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Q: 4. Evaluate the double integral: So Sa+1 ¹/3 27 +1 (Hint: Change the order of integration to dy dx.)…

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Q: 7 Find the general Solution of the following PDES. -X • 3U XA2 Uy so > u(x,0) = 4 ex (3y-2x)/2 ans -…

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Q: Find the general Solution of the following PDES • з Их + 2 Иу , u(x,c) = чех (3У-2х)12 ans3- исх, у)…

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Q: 7. Compute the area of the region R enclosed by the curves y = x² - 1 and y = 1- x.

A: We have to find out the area

Q: d/dx [x/(x^2 + y^2) ] = * O [(y^2 + x^2)/(x^2 + y^2)^2 ] O -[(y^2 +x^2)/(x^2 + y^2)^2 ]…

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Q: xe. xe2x dx

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Q: Find the taylor series of the following functions for the given points:- 2- f(x)= sinx a= π/4 3-…

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Q: The equation P= 15 sin (2nt) +90 models the blood pressure, P. where t represents time in seconds.…

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Q: ar the function A whose graph is shown, state the following. (If the limit is infinite, enter 'n'…

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Q: Set-up the iterated double integral in polar coordinates that gives the volume of the solid enclosed…

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Q: H.W Find the taylor series of the following functions for the given points:- 5- f(x)= a=0 x+2

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Q: Given that f(z) = z-z where does f'(z) exist

A: Concept: z  is represented as  z=x+iy And its complement z¯ z¯=x-iy For f'(z) to exits only if…

Q: find the integral from 1 to 4 of (3t^(3/2) i+(t+4)(√t)k)dt

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Q: ¹ ( 7 (x − 3)). Consider the function f(x) = 4sin((x-3) +6. State the amplitude A, period P, and…

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Q: 2. Evaluate the Integrals using the Fundamental Theorem of Calculus. 1. S/4 cos x dx π/4 2. ¹₁ sec²…

A: First I have written the Fundamental theorem of Calculus, using it for given integral and find its…

Q: Determine the values of r for which the differential equation y" - 4y = 0 has solutions of the form…

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Q: ♥ дzu ахбу = сезх созу, Ans: u(x,y) = sinx siny + x² + 2 cosy - #2² X 1 бу исx;#) =X бx U(x,п) =X,…

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Q: from the date set, find the value of f(7) by use lagrang method X 3 6 9 11 y 12 13 14 16

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Q: What are the domain, range, and period of the function f(0) ) = -20cos( - 10) + 1₂

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Q: Q4: A) For each of the following ,find fx fy fxx fyy fyx and fxy 1.f(x, y) = ln(2x + 3y). 2.f(x, y)…

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Q: 2 убличк In'/xl alx

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Q: 6. 8 2 2 dv 2 v - v V

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Q: àtics II, e the caraid Q3) By using the polar find region enclosed by y = x² and y = 1 Find the

A: Let's find region enclosed by curve and given line.

Q: Function h is graphed. h -4 -3 -2 L y 4 3+ 2- 1 -1- -2+ -3- 12 3 4 Find h(2) da. Give an exact…

A: This question can be solved using the concept of area under curve.

Q: 2+x a) lim x-22+x²

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Q: find the Fourier series of half rang periodic function. f(x) = x|x| -π < x < π <x<π

A: We know the following. Fourier series of function fx on interval -L≤ x≤ L is defined as:…

Q: 1) Find the absolute maximum and minimum for function f(x,y)=x²-xy+y²-6y-4, on the domain -4≤x≤2,…

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Q: find the solution of following differential equation using Laplace transformation. y" + 3y + 2y = ex…

A: Let's solve given diffrential equation by using laplace transform.

Q: 2 =(x² - 1)³/²,1 ≤ x ≤ 3

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Q: find the given differential solution, using homogeneous equations with constant coefficients.…

A: Given:y''+2y'-3y=0