Find the sum, if it converges. Σ6 i= 1 The sum is (Type an integer or a simplified fraction.)

Q: Find the Laplace Transform of the given function using the definition of Laplace Transform a. f(t) =…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Given r = (5, 2, 3) and s = (-4, -2, 2) and t = (3, 4, 1) %3D a. Write the unit vector for S b.…

A: This question can be solved using the concept of unit vector and linear combination of vectors.

Q: 5.) Find the volume generated by revolving the area bounded by the curve y2=4x, x = 0 about the line…

A: Given area is bounded by: y2=4x and x=0. The area is revolving around the line y=4. From y2=4x we…

Q: Find the sum of the first n terms of the following arithmetic sequence. a1 = 2, d = - 4; n = 6 O A.…

A: Given problem:- a1 = 2 ,d = -4 ,n=6  To find:-  Sum of n terms of given arithmetic sequence

Q: Describe the applied transformations from y = 32 to %3D graph the function g(x) = -2(3)-2x-6 + 9 %3D

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Q: Find the standard equation of the sphere with the given characteristics. Center: (-1, -9, 6) Radius:…

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Q: 3n4 Σ Consider the series > 6n4 + 2 n=1 Based on the Divergence Test, does this series Diverge?…

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Q: 1. Given the General Solution the DE, Identify the roots * y = C1e4* + C2e¬* + C3 O A) m1= 4; m2= 0…

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Q: ) Syppose f and g are functions with continuous lerivatives, and that they satisty the following. S…

A: Let's find.

Q: Find V x (V x F) if F(x, y, z) = 9xyj+ 5xyz k. V × (V × F) :

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Q: Find div F and curl F if F(r, y, z) = 2e*"i– 9cos yj+ 4 sin² z k. div F= curl F=

A: Given: F(x,y,z)=2exyi-9cosyj+4sin2zk

Q: he Taylor series for fx) centered at the given Val f(x) = x- 6x2 + 2, a = 2 %3D E"e(x- 2)" = -6 +…

A: Taylor series

Q: Use a triple integral to find the volume of the solid shown in the figure. z = 16 – x2 - y2 130 10…

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Q: III. Do as indicated showing the details of your work. Show your complete solution on the space…

A: We need to evaluate definite integral.

Q: Find div F and curl F if F(r, y, z) = 2e""i – 9 cos yj+ 4 sin? z k. div F= curl F

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Q: 26) In Problem 26 and 27, given f(x)dx= - 1 J g(x)dx= 2 and S f(x)dx= 3 a a d. Find f" f(x)dx + S*…

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Q: Find curl (2z i + 3x j + 5y k). curl (2z i + 3x j + 5y k) (i )i + ( i j+ ( i )k

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Q: Solve the differential equation Bernoulli Equations: dy + бу — Зху3 dx 4 3xys

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Q: Use the Table of Laplace Transform to find the Laplace Transform of the given function. a. te-3t b.…

A: As per our guideline, we are supposed to answer the only first question with 3 subparts to get the…

Q: If the price charged for a candy bar is p(x) cents, then x thousand candy bars will be sold in a…

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Q: dy 4 + 4y = xe'

A: To solve the differential equation by using method of undetermined coefficients.

Q: am confused can you highlight answers please thank u

A: From the original solution the answers are: Intercept: 0, 0 Relative minimum: -5, -110 Relative…

Q: Solve the area bounded by the curve y = 4x - x² and the lines x = -2 and y = 4.

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Q: Give the representation, equations and solution. Use elimination, comparison or substitution to…

A: Let, First number = x & 2nd number = y therefore, x+y=25   & x-y= 7

Q: 3. A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine containing 1…

A: Given problem:-  A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine…

Q: The sum of the digits of a three-digit number is 11. The tens digit is three times the hundreds…

A: Let a be the hundreds digit, b be the tens digit and c be the units digit. Thus our required three…

Q: 7. lim vx2 + x + 1 – Vx2 + 1

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Q: Set up (but do not evaluate) an iterated triple integral for the volume of the solid enclosed…

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Q: Describe the graph of the equation. r = (7 – 21) i+ 101j O Itis a line in 2-space through the point…

A: Equation

Q: Solve the differential equation Integrating Factor by Linear Equation: y' = 1 – 2ycot2x

A: We can solve this as follows:

Q: Evaluate the expression. 14C11 O A. 182 В. 3003 О с. 2,184 O D. 364

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Q: 5. lim X-0 e2x-1

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Q: Answer

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

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Q: -Find Taylor or Maclaurin for the following functions: 3) 2) f (x) = e* at a = 2

A: A detailed solution is given below.

Q: Describe the graph of the equation. r = (5 – 21) i + 71j O It is a line in 2-space through the point…

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

Q: Find each of the two areas bounded by the

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Q: Solve the differential equation. dr sin 0- do +(cos 0)r = tan 0, 0<0<,

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Q: Give the representation, equations and solution. Use elimination, comparison or substitution to…

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Q: Find div F and curl F if F(x,y, z) = x°i – 2j + yzk. div F= curl F=

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Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 4x?y – 6xyz + 10yz2…

A: Given problem:- Find the first partial derivatives with respect to x, y, and z.   f(x, y, z) = 4x²y…

Q: Solve the differential equation Integrating Factor by Linear Equation: dy — у — 5х* — Зх? + 2х — 0…

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Q: 6. lim (sinx)*

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Q: 1 Without a table of values and using index laws, sketch y 2*-

A: y=12x 2-1 y=12x2 y=22x

Q: 2. SET-UP the definite integral that will give the area of the region specified using (a) x as the…

A: Area

Q: Evaluate the indefinite integral. (Use C for the constant of i | sec?(e) tan°(e) de

A: Topic:- integration

Q: Evaluate the double integral. / 5x(4 + y) dA; R R is the region in the first quadrant enclosed by y…

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Q: sin(3x) dx 1+cos²(3x)

A: The given integral is Sin(3x)/[1+cos2(3x)].

Q: I. INDETERMINATE FORMS: Evaluate the limit by employing Theorem 23. f(x) f'(x) lim = lim Equation 1…

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Q: A particle started to move from the origin along a curve with velocity given by the function v(T) =…

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