P-4 Use separation of variables to find the product solution of the following a) ди ди b) J2u 02u y 0 = ?х +x= ду дх2 at² = q2

Q: Jse differentials to approximate 47. (Express as a rational number.)

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Q: Consider the function 2x+6 f(x)= x²+6 Find the critical point(s) off. (Give yourans wer in the form…

A: f(x) =(2x+6)/(x2+6)  Find:- Critical points  Local maximum and minimum at x= Interval function…

Q: Estimate the slope of the tangent line to the curve at the given point (-0.5,4.998) on the graph to…

A: Given that,

Q: S dx √1-x² O-√1-z² sin-¹ z²+z+C O-√1-² sin¹z+z+C O None of the choices O-In 1-2² | sin¹2² +2+C -1…

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Q: Evaluate the iterated integral. 40 (xªy-7xy) dy dx 0-4 40 jjov (xªy-7xy) dy dx = [ 0 - 4 (Type an…

A: The given integral,    ∫04∫-40x4y-7xydy dx

Q: Determine the equation of the ellipse with center (7, 1), a focus at (2, 1), and a vertex at (-6,…

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Q: Calculus optimisation problem Amount of fuel 'F' (in litres) required per hour to propell his…

A: Given, F(u) is the fuel in liters required per hour. u is the speed in kn/hr u(max)= 40 km/hr F(u)=…

Q: Find the unit normal to the surface z=2+2z^2-3y^3 at the point (1,-1,7), pointing down with respect…

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Q: At noon, ship A is 30 nautical miles due west of ship B. Ship A is sailing west at 22 knots and ship…

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Q: Evaluate the integral. (Use C for the constant of integration.) +² | dx 81-x²

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Q: Given [ƒ(x) a f(x) dx = -5, and g(x)={3x+2,355 / 3x+2,3≤x≤5 integral. Find the value of k that…

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Q: The height (feet) of a ball launched in the air t seconds after it is launched is given by: f(t) = -…

A: Given query is to find the the velocity when height is 120 ft.

Q: intervals. (a) [1,2]n (1/2,2) n (0,1/2]. (b) R-(0.3) (c) (-2,0) U(-1,5) (d) (R-(0,3)) ((-2,0U(-1,5))

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Q: 4. f(x) = 5. f(x) = 6. f(x) = 2x+sin x x sin x 2x²+x x sinx+2 sinx 2x²

A: Solution

Q: Q3: Find the solution of the Laplace transforms of the following functions: -3s²-12s-87 L-1 1)…

A: Let's find laplace inverse of given function.

Q: 3 The absolute minimum value of f(x)=x³ on the closed interval [-1,8] is a) 0 b) -1 c) 1 2 d) -…

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Q: what happened to the 1(1-lambda) part in the first line

A: Given

Q: Find Hence evaluate d dr 1 Š S ₁ (1 +2²2)³/26 0 -1 1+x², dx.

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Q: Find the determinant of the matrix, show all of your work -1 3 5 0 0 1 -2 000000 4 0

A: We need to find the determinant of the following matrix. So,…

Q: The interval of convergence of the following Power Series +∞ Σ nxn 4¹ (n + 1) n=1 ]-4,4] [-4,4]…

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Q: Using the definition of the derivative, find f'(x). Then find f'(1), f'(2), and f'(3) when the…

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Q: We are interested in the first few Taylor Polynomials for the function f(x)= 7e + 3e-* centered at a…

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Q: Verify that * ox af dy 2+ ?х ду ду дх ах 22+ 21 ?х ду ду дж 11 olems) for f(x, y)=5x®y -7xy5.

A: Here is the solution of the given problem.  Partial Derivatives.

Q: Find an equation for the plane that is tangent to the surface z = In (x+y) at the point P(0,1,0).…

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Q: Use the law of cosines to determine the length x in each figure. Leave your answers in terms of…

A: The law of cosine is: c=a2+b2-2abcos C

Q: Determine all solutions of the given equation. Express your answer(s) using radian measure. (Select…

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Q: Given [ƒ(x) dx = -5, and g(x)= {x²-1,0≤x≤3 . Using the properties of (3x+2 ,3≤x≤5 integral. Find the…

A: Ans= -20  For detail...go through the solution...I have solved using given information in detail

Q: Evaluate the integral 3 -x a. So Sox² exy dydx 0

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Q: Determine the amplitude, period, and phase shift for the given function. y = 1 cos 2x - cos(2x - 3)…

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Q: 5) Write the equation of the line through the points P(1,3,7) and Q(2,5,11) in: a) Vector form b)…

A: topic - equation of line through two points

Q: Calculate M6 for f(x) = √7x on [0,2]

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Q: Л ST 6 77 6 EN F/3 2 3 -0 i 11 6 4) V3 2² 2 27 3 F|N 11 6

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Q: A street light is at the top of a 13 ft tall pole. A woman 6 ft tall walks away from the pole with a…

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Q: Homework: MML 1.1 T Line Find the slope and the y-intercept of th y=6-2x Select the correct choice…

A: Given query is to find the slope and y intercept of the line.

Q: S dx . Consider ½/₂ Using rationalizing substitution, what will be z and its corresponding integral?…

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Q: 2. Find the limit and confirm your answer using the sandwich theorem 1 - cos x lim 818 1. 2. 3. 4.…

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Q: O The series Σ7-"[2 +5¹] n=1 converges to none of the choices the above converges to converges to…

A: The above series converges to

Q: The sum of two positive numbers is 20. Find the numbers if the product of the square of one and the…

A: topic- application of derivatives

Q: 8y^4+12y^3-2y divided by 2y^2+y

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Q: 3. 13 dr² +9y= 26e2r

A: The given differential equation,     d2ydx2+9y=26e2x

Q: List the first five terms of the sequence. - 1. a₁ = 2, a₂ = 1, an+1 = an an-1

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Q: 2 1) x² + y² + 18x - 26y+246=0 CX+972+(₂-137² = 4

A: As per the guidelines we are supposed to answer only one question at a time. If you want answers of…

Q: Set up the definite integral required to find the area of the region between the graph of y= 2²-12…

A: find intersection point

Q: Find the volume of the solid of revolution generated by revolving the region bounded by the graphs…

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Q: A(4) = A'(4) -

A: Integration gives area below curve area above x axis is positive area below x axis is negative A(4)…

Q: a) Find the derivative in its simplest form for the following function 1–tanx y = tan-1 ¹

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Q: I. EVALUATE THE FOLLOWING LIMITS. SIMPLIFY AND ENCLOSE FINAL RESULTS. 5. Lim xsinx x→ 0+ 5

A: solution:-limx→0+xsinxwe know that binomial expension of…

Q: 4. Convert the following rectangular coordinates to polar coordinates, then find 3 additional repre…

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Q: 4. Find 3x 2t dx/e²t dt

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Q: Find area inside 3 - 3 cos 0 and outside r = 3

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