Calculate the first, second, and third derivatives of y(t) 101 – 512 + 2. %3D (Use symbolic notation and fractions where needed.) y (1) = y"(t) = y"(1)

Q: b) Solve the given homogeneous differential equation subject to the indicated conditions. y" + 2y' +…

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Q: Q2 Obtain the general solution for the following differential equation. b) y" – 4y' + 3y = 3e2x +…

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Q: 3. Which of the following is always true for any real numbers x, y? For real e > 0, if Ix-yl se,…

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Q: Suppose that z = xy² and x and y are differentiable func- tions of t with x =2,y = when t = -1. Then…

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Q: Q1) A) Find the tangent equation for the function: f(x) = Vx2 + 5 at x=2? %3D

A: To find the tangent equation for the given function.

Q: If possible, find AB. (If not possible, enter IMPOSSIBLE.) 0 1 0 B = 3 1 A = -5 5 0 4 2 1 8 6 -1 7…

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Q: - Ose the tranfiorms from the "Table of Lapiace Transformso fnd the Lpce of the function below. You…

A: Given problem:- Find the laplace transformation of f(t) =(1+t)3

Q: Find the arc length of the polar curve described by: r = 5+ 5 cos 0

A: Use the formula for the arc length in polar coordinate.

Q: B) Find the limits by using L.Hopital rule : 7x 1. lim x0 sin 2x x2-16 2. lim x-4 (Vx+5)-3

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Q: 2. a) Determine the coordinates of all point(s) on the graph of y = 2x In x where the tangent line…

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Q: Solve for the indicated higher-order partial derivatives, fæx, fæy, fyy- · f(x, y) = Vx² + y?

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Q: The line given by r (t)=(14+5t, -3t, 1+7t) and the line given by r(t) =(3-3t, 5+2t, -2+4t).

A: Follow the procedure given below.

Q: Given the e dz nd y, find ar

A: Given: xlny=zArctan3zy

Q: Which of the following is not used to determine the slope of a function algebraically? slope of…

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Q: Q2) Find the integral value for the following functions dx 4. S x2Vx2-1 eCos-1x 5. S V1-x2 6. Se…

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Q: 8. Let 7 (t) = < - 2 cos(8t),- %3D Find fF(t)dt (don't include the +C) frona -

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Q: Prove that lim 1 1 by definition.

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Q: Q2) Find the integral value for the following functions 3x 1. S 2. S(sec(4x) – 1)² dx 3. S dx V1+3x2…

A: The integration of the integrals is  1) 3x/sqrt(1+3x2) 2) [sec(4x)-1]2 3)1/[1+(5x+1)2]

Q: The system is a two-dimensional coordinate system in which each point on a plane is determined by a…

A: To fill the gaps using the given options.

Q: Find the exact arc length of the curve over the stated interval. y = 3r/2 – 4, from a = 0 to a = 1…

A: This question can be solved using the formula of arc length.

Q: 1. Find an equation for a parabola with focus (– 10, 7) and directrix x = - 6.

A: A detailed solution is given below

Q: A. Solve the following problems using the concepts of Parametric Equations. Show complete solutions.…

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Q: Match the vector field with its graph. F(x, y) = yi 5 -5+ 5 5 5 -5+

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Q: 3x2 dx x3 COS xesinx -5 a) b) dx c) 4x dx esin a X-4 1 /n

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Q: Find the general solution of the following linear second order inhomogeneous O.D.E.: ý - y = e*

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Q: Q4) Find for the following functions (- dx Зх +4 %3D 2x+3 6. y = tan-1 V4x3 - 3 %3D

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Q: B) Find for the Implicit function: dx x² – sin(xy) + y² = 5xy %3D

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Q: Find T(t) and N(t) at the given point. r(t) = (t? – 3)i + tj; t= 3 T(3) N(3) =

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Q: Approximate the integral using Taylor series method: xsin?x dx

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Q: Find the area of the region under the graph of the following function. f(x) = 5xe−x from x = 5 to x…

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Q: Use Chain Rule to find given w = ds x2 – 2y + z2 and a = cos (st), y = -2s In t and z = s – - VE.

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Q: Set up the definite integral required to find the area of the region between the graph of y 15- and…

A: Area between the two curves f(x) and g(x) over the integral [a,b] is given by A=∫abfx-gxdx

Q: B. Solve the following problems using differentials and linear approximations. Show complete…

A: (a) The given function is: f(x)=x3 The formula for the linear approximation at x=27 is given by:…

Q: If y = f(g(h(x))), then the derivative y/ is given by which formula? a) None of these Ob) f'(g(h(x))…

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Q: Question Use the second Taylor polynomial for f(x) = e" at x = 6 to estimate e7. Round your answer…

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Q: Use any method to determine if the series converges or diverges. Give reasons for your answer. Σ…

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Q: Find the area of the region enclosed by the curves y=x^2 and y=6x by integrating with respect to y.…

A: To find the area of the region enclosed between the two curves.

Q: 12. S,(s² – 1) sds 13. (1² - t) dt

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Q: 1. Identify the type of conic section whose equation is given, then find the vertices and foci.…

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Q: x³y' – y? – x²y = 0

A: We have to integrate the above expression

Q: The solution of the initial value problem: 1 dy X +1 dx 1 for which y(1) = 1 is y

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Q: Select the conic section represented by the equation. 2x + 5y - 7 = 0 circle ellipse point line…

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Q: Let C1 be the curve with parametric equations x = cos t, y = sint – t, where t e [0, ). (a) Find the…

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Q: Evaluate F. dr. F(x, y) = xi + yj C: r(t) = (3t + 4)i + tj, 0 <t<1

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Q: (а) у"— (а + В)y' + аBy %3D 0 (а + B)

A: Answer as follows

Q: 1. Rule 1: Add 2 starting from 9. Rule 2: Add 3 starting from 5. Sequence 1 Sequence 2 Ordered Pairs

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Q: When a factory operates from 6 AM to 6 PM, Its total fuel consumptlon varies according to the…

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Q: Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep…

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Q: Q1) A) Find the tangent equation for the function: f(x) = Vx2 + 5 at x-2? %3D

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Q: Find for the Implicit function: dx x2 – sin(xy) + y? = 5xy

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