II. Find the Inverse Laplace of the following 1 a. s² +6s+25 s2 b. (s-1)3 7 C. s4 8 - - - s3 s2

Q: Find V (F x G), if F(r, y, z) G(x, y, z) = xi+ yj - zk. = 2xi +j+ 8yk and V. (F x G) =

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Q: 13) Determine the lim X--9 + 169 く+9

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 8 1 lim t++o \ 5t2 + 6' 5t (0,0)

A: Simplify the component wise

Q: Solve for the derivative of the following composite functions. f(g(x)) = (x + 4)5 1.

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Q: Which integral corresponds to the volume of the solid generated by revolving the region enclosed by…

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Q: b. In x? dx

A: According to the company rule we can answer only first question and rest can be reposted.

Q: Find the limit. NOTE: Enter the answer using round brackets. t2 +8 1\ lim t++o \ 5t2 + 6'5t (0,0)

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Q: 3) Find and d²y of the following equation then simplify whenever possible. dx dx² x = 3em y = 2mem

A: A detailed solution is given below

Q: Evaluate the integral / (2x + 12y)dx + (24x – y)dy along the parabolic arc y = x² from (0,0) to…

A: For the arc y = x2 and the range of x from 0 to 1. So, dy = 2x dx. Now,…

Q: 1.) Find the area bounded by the curve y?= 1 - x and 2y = x + 2 2.) Find the area bounded by the…

A: Solution is given below:

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

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Q: Evaluate the integral / (2x + 12y)dx + (24x – y)dy along the parabo arc y = x² from (0,0) to (1, 1).…

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Q: Complete the squares and locate all absolute maxima and minima, if any, by inspection. Then check…

A: We will do partial differentiation to find maximum or minimum point

Q: d,x+7 3. dx 2x-3

A: To find: ddxx+72x-3

Q: 3. Find the values of x of the curve y = 3x where y' = y" 15

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Q: The sum of one number and five times the second number is 50. A. What are the numbers so that their…

A: Let the first number be 'x' second number be 'y'. A/q  x+5y=50⇒5y=50-x⇒y=50-x5 The product of first…

Q: Distinct Real Roots of Auxiliary Equation the general solution (D² – 9)y = 0 (D² – 1)y = 0 -

A: Topic:- solution of differential equation

Q: Evaluate the double integral. 7x sin y'dA; Ris the region that is bounded by y = x², y = -x', and y…

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Q: ||r(t) × r"(t)|| ||r(t)||* Use the formula k(t) to find k(t). r(t) = 11 cos(8t)i+11 sin(8t)j+ 3tk…

A: r(t)=11cos(8t)i+11sin(8t)j+3tkr'(t)=d11cos(8t)dti+d11sin(8t)dtj+d3tdtk=-88sin(8t)i+88cos(8t)j+3kr''(…

Q: Ow dw Find dx' dy and dz using implicit differentiation. Leave your answers in terms of x, y, z, and…

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Q: Find the indefinite integral. (Use c for the constant of integration.) (4t3i + 14tj – 6/tk) dt

A: we have to find the indefinite integral

Q: Each of the following statements is an attempt to show that a given series is convergent or…

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Q: Using the Nth term test for divergence 5 1 n=1_2n +14 5 diverges since lim is equal to 1 2n+14 O 1/3…

A: We can answer the question as below.

Q: Find the partial derivative. f(p, q) = e=

A:

Q: Describe the domain and range of the function. f(x, y) = 3x2 – y Domain: O (x, y): x = 0, y = o…

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Q: A line, passing through point (6, 3, 2) and is perpendicular to the xy-plane. Find a point on this…

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Q: Find div F and curl F if F(x, y, z) = 13y°z³i – 9x*z³j – 4ry°k. div F= curl F=

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Q: Find the exact length of the curve. y (y-3), 4sys 16 X =

A: use derivative for finding the exact length.

Q: Find the exact area under the curve between the indicated values of x. y = between x = 1 and x = 4…

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Q: Find the arc length of the parametric curve. x = e', y = et, z = v2t; 0<t< 7 L = e - e- - 0

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Q: Evaluate the integral. 2 (3u - 5)(u + 2) du -1

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Q: For the given vectors a and b, find the cross product a x b. =(3,0, -1), b = (3, 2, 0) a %3D a x b =

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Q: Take

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Q: Use the formula «(t) ||r'(t) × r"(t)|| to find «(t). r(t) = e12i + e-j K(t) = %3D

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Q: Using the fundamental theorem of calculus, find the derivative of the integral -3x+2 t -dx 1+t3

A: We have to find derivative of given function.

Q: 8 – a? if – 2 2 between O 8 and 16 O O and 8 O 16 and 24 O 16 and 33

A: Given problem:-

Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(1) = i – 26j + %3D (a) r(t) 3ti- 2j + 2 k (b)…

A:

Q: Solve for k such that 1 | k(x² – 2x + 1)dx = 5

A: Given problem:- ∫ k(x2 -2x+1) dx =5  Solve for k

Q: x 1 What is lim f(x)? x→-1 O 3 O 4 O 2

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Q: 5. y = (x+7)(5x- 2)

A: Given : y=(x+7)(5x-2)   To Find : Derivative of the given function.

Q: function f has the following graph: 4- 3 2 1. -1 6 7. 8 -1 -2 Vhich of the following is true? O The…

A: Given query is to find the correct statement for the function.

Q: Find r'(t), r"(t), r(t)•r"(t), and r'(t) × r'"(t). r(t)-흑러 - 26 + (a) r'(t) (b) r"(t) (c) r'(t) ·…

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Q: 20 u(x) = 0.3e(0.5(-x+ 275.1)) + 3.62 21 v(x) = -1.2 log, (0.3(x – 269.73))+4.4

A: We need to find derivative.

Q: I. Evaluate the following Definite 1.) Sº 6x³+4x²-8x 1.) L,º 2x 3) (3 sin3(x)dr

A: According to rules.. I  need to solve 1st question

Q: Using appropriate substitution | sec*x dx is equal to In|secx + tan x| -1 + C 2cos?x + sec x tan x +…

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Q: ind the arc length oI the parametric curve. 0 = 6 cos (t), y = 6 sin(t), z = 8t; 0 stST

A: Given: x=6cost, y=6sint, z=8t

Q: For the given cost function C(I) = 128/ + find 512000 d) The production level that will minimize the…

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Q: cx2 + 8x if x < 3 Let f(x) = 1 x3- cx if x 2 3. For what value of the constant c is the function f…

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Q: Describe the graph of the equation. r = - 2i + tj + (t² – 1)k O Itis a parabola in the x = 2 plane,…

A: Here we  have to identify the vector.

Q: A differential equation is considered to be ordinary itit has one independent variable None of the…

A: