6. Differentiate: a. f(x) In (In (3x)) b. Find equation of the tangent line to the graph of y-e³x. lan (4x) at x = 1.

Q: = Let f be a function defined for t≥ 0. Then the integral L{f(t)} . - fotº e- 0 provided that the…

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Q: Find the area of the region bounded by the following curve. The limiçon r= 6-4 cos 0

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Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

A: Our Aim is to find the inverse Laplace Transform of the following function given…

Q: S √√x+12 X S- dx using substitution. √√x+12 c. Verify that your answers to parts (a) and (b) are…

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise. $…

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Q: (a) ах = Du DE = du, ada voa waye by oz + + + 2x DE 2. (x²= y² + x) x (2x+₁) + (-2xy-9)x (-2y) (2x +…

A: We have to simplify (x2 - y2 + x) × (2x + 1) + (-2xy - y) × (-2y)

Q: Which equation of a circle has the center, C, and radius, r, as shown in the graph? -3-2 7 T of 7 T…

A: The circle has center C3,-2 and radius 26

Q: Find the derivative of the function. f(x) = arcsec(4x) f'(x) = 4 4π√ 16x² - 1 :or 1 xV 16x²-1 2

A: Topic = Derivative

Q: Find the equation for the slope of the tangent line to the curve below at any point (x,y). 2x + 5y =…

A: Given, 2x+5y=3y

Q: Use the Alternating Series Remainder Theorem to determine the smallest number of terms required to…

A: To use alternating series remainder theorem to determine the smallest number of terms required to…

Q: The population of Toledo, Ohio, in the year 2000 was approximately 480,000. Assume the population is…

A: This question can be solved using the concept of general form of exponential growth function.

Q: Solve the system using Cramer's Rule. 2x + 5y = -25 -x+3y=-4 Find the determinant D (denominator).…

A: Please refer to the image below

Q: Consider the following function. f(x)=√x-9, x> 9 What is the domain of f? (Enter your answer using…

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Q: On (-∞, ∞), three functions y₁(x) = cos 2x, y2(x) = sin² x, y3(x) = cos²x are linearly independent…

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Q: ground is given by the function s(t) = - 16t² + 47. Round values below to 3 decimal places. How long…

A: Please refer to the image below

Q: Use Definition 7.1.1. Definition 7.1.1 Laplace Transform Let f be a function defined for t≥ 0. Then…

A: Break the limits according to f(t)

Q: Let f be a function defined for t 2 0. Then the integral {f(t)} =[e-stf(t) dt is said to be the…

A: We need to find Laplace.

Q: Given: f(t) = 8 t 2 Evaluate: F(2) Round-off answer to 2 decimal places.

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Q: 3. Express the integral I = f(x, yz) dV as an iterated integral in three different ways, where E E…

A: Solution is given below:

Q: Use the definition of Taylor series to find the Taylor series, centered at c, for the function. f(x)…

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Q: (Q8.6) Choose five other iterated integrals that are equal to the given iterated integral. 10 10 10…

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Q: 3. Find the value of (T) for a solution (x) to the initial value problem: y" + 25y = 10 cos 5x; y(0)…

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Q: Jxy co R xy cos y dA R: -1≤x≤ 1,0 ≤ y ≤

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Q: Question Find the linear approximation L(x) of the function f(x)=√x - 10 at a = 26. (Enter an exact…

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Q: Determine whether the equation is exact. If it is exact, find the solution. (e'siny + 3y)dx -…

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Q: 21. If u = - y+z a) 0 Z z+x x+y b) 1 ди then the value of x + y + z 2 is: c) u d) None 22. The…

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Q: Consider the function f(x) = 1 - 2x², -4≤ x ≤ 2. The absolute maximum value is and this occurs at x…

A: Given: fx=1-2x2, -4≤x≤2   As we know the Power law: ddxxn=nxn-1 For maximum and minimum values,…

Q: 1. Determine the value for the number "a" so that lim x-2 3x² + ax + a +3 x²+x-6 will exist. Also…

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Q: What is the gradient of f(x, y, z) = x³z2 + y³z +125z - 1 at P(5,5,-1) ?

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Q: 1 Σ (3)"-wn + 4 n = 0 (n + 1)(n + 2).

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Q: Find curl(4z i+ 5x j + 7y k). curl(4z i + 5x j + 7y k) = ( i )i + ( i )j + ( i )k

A: Topic- Curl of a vector

Q: Answer true or false. If f is not piecewise continuous on [0, co>), then L{f(t)} will not exist.…

A: The given statement is

Q: S- - ydx + xdy, C: y² = 3x from (3,3) to (0,0) 01 0 3 O 0 2

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Q: 20 29t2 +42t represents the position function for a particle moving The function s(t) = along a line…

A: The given function is: s(t)=203t3-29t2+42t  where t∈0, 6 v(t)=d(s(t))dt=d203t3-29t2+42tdt=20t2…

Q: Evaluate the limit using L'Hopital's rule. Enter either a reduced fraction or DNE. lim 7…

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Q: 3. Pedro walks at te speed of 40 meters/min from the school to home, by taking the longer route of…

A: Pedro walks at the speed of 40m/min from the school to home,by taking longer route of 100 m to the…

Q: Find the curvature and the radius of curvature at the point t = 0. et cos(t), y et sin(t), z = 9et K…

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Q: Problem 5.3. Solve the following differential equations by regarding y as the independent variable…

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Q: Determine the y-coordinate of the centroid of the shaded area. bl. | x=y²/b b Answer: y = i 0.48b MI…

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Q: Solve the given differential equation. All solutions should be found. 2xy + y² + 1 x² + 2xy dy dx…

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Q: Find the equation for ​(a) the tangent plane and ​(b) the normal line at the point P0(1/2,1,e) on…

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Q: For the function f(x)=ln(1−5x)​, find the Taylor polynomials of orders​ 0, 1,​ 2, and 3 generated by…

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Q: Sketch the region D of integration, and then evaluate the integral by reversing the order of…

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Q: Convert the following equation to Cartesian coordinates. Describe the resulting curve. r = 4 cos 0 -…

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Q: Find curl (62 i + 7x j + 2y k). curl (62 i + 7x j + 2y k) = (i )k )i + (i )j + ( i

A: Here we have to find the curl.

Q: Newton's law of cooling states that the temperature of an object changes at a rate proportional to…

A: I am attaching image so that you understand each and every step.

Q: The area under one arch of y=sin(0.5x) is O 0.2 O 0.5 O 0.8 None of them

A: Given: y=sin(0.5x)

Q: Find the value of() for a solution (x) to the initial value problem: y"" − 3y" + 4y' – 2y = 0; y(0)…

A: In this question, we want to solve the third order homogeneous differential equation.

Q: 1 2.5" y 3" 6 -Х

A: Given data:-

Q: The eigenvalues of a square matrix A are the numbers À for which the matrix A-XI is regular.

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