Peaive marima and, minima, 4 any tar the funchno If there is not an answers write N/A Wde ms wefs as aldered paies. the calative tos %3D 2.

Q: Determine whether the improper integral converges and, if so, evaluate it. (Use symbolic notation…

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Q: Find the surface area of a sphere at the instant when the rate of increase of the volume of the…

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Q: dy y- 2x. dx = x(x+1)y %3D

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Q: Determine the following Laplace transforms: (i) mathcal L \ cos^ 2 3t\ .

A: Given

Q: Fibe the graph of the equation. = (7 – 21) i + 10tj r = O It is a line in 2-space through the point…

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Q: Find V· (F x G), if F(x, y, z) = 10xi +j+7yk and G(x, y, z) = xi+ yj – zk. V · (F × G) =

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Q: Find V x (V × F) if F(x, y, z) = 5xyj+ 10xyz k. V × (V × F) =

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Q: 5x? + 8x + 3. If Aæ 0.3 at x = 5, use linear approximation to estimate Ay Let y Ay =

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Q: 1. A bumblebce was released and started to travel along a straight horizontal line. The directed…

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Q: Let h(x)= f(g(x)) where f(x)=tanx. Then h'(x)= a) f'(tan x) g'(x) b) g'(x)tan(g(x)) c) g(x)…

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Q: 1) Center: (12, -3) Radius: 3) Center: (-4, 10) Radius: 8 5) Center: (-3, 9) Radius: 8

A: 1) center: 12,-3Radius: 33)center: -4,10Radius: 85)center: -3, 9Radius: 8

Q: 16 d :| (2V8– 1) dt da. valuate dr. dx 5.

A: We have evaluate to the given expression

Q: Evaluate the line integral / (4x + 8y)d.x + (4x – 9y)dy along the curve C : x = 10 cos t, y = 20…

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Q: Solve the system of equations using matrices (row operations). 3z- 3w = - 4 X+ y+ z+ 3w= -1 2x + y-…

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Q: Show that \{e ^ (- x), x * e ^ (- x)\} is a fundamental set of solutions of y^ prime prime +2y^…

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Q: Evaluate the line integral -ydx + xdy along the curve C : y? = 30x from (30, 30) to (0, 0). %3D…

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Q: 6x° – 15x* + 20x – 1 and classify them using a Find the critical numbers of the function f(x) =…

A: Given the function

Q: 8. 1 +3 + 3² + . + 3"-1 = (3" - 1) (3"- 1) ...

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Q: Find curl(2: i + 3x j + 6y k). curl(2: i + 3x j + 6y k) = ( )i + ( j + ( )k

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Q: Find V· (V × F), if F(x, y, z) = 5e**i+ 5xe®j – 7ev³k. V· (V × F) =

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Q: 1. Suppose you are in charge of payouts for a competitive 10K race. You decide that the top 12…

A: (A) Solution:  In both options total amount is same i.e. $546,000 but option B situation will be…

Q: Consider the curve parameterized by x 3t2 15 and y 2t 15. Find equations for all tangent lines to…

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Q: | sin³(18x) dx =

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Q: Find all real and complex solutions to the equation   x^3 − 3x^2 − 10x + 24 =0

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Q: 4. Find lim (sin¬ V)cschr. r0+

A: The given limit,         limx→0+sin-1xcschx

Q: Find the total area bounded by the x-axis and the curve y = f(x) on the indicated interval. Enter…

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Q: Given x sin 4t and y = cos 4t, find the following derivatives as functions of t .

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Q: Find T(t) and N(t) at the given point. r(t) = 6 cos(t)i + 6 sin(t)j + tk; t= 2 6 0 , V37 1 T V37…

A: SEE EXPLANATION

Q: Find the deriva tive Of 6- sin (xy)+ e'

A: Note:- It is not mentioned in question for derivative find with respectvto what variable(x or y) so…

Q: Test the convergence of cach of the following two scrics. n" 2n +3 (1) 2 n! (ii) Зп + 2 n=1 n=1

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Q: II 2. 3. 2. 4. x² 1. X. 3. D3x 4. 1. Find the given derivative. 4-part 1 Homework: Homework Chap

A: Dx3x-12 + 4x32=Dx3x-12 + 4x-32                               =3Dxx-12+4Dxx-32…

Q: Solve the following differential equations of >(3x² – 6.xy)dx +(-3x – 2y)dy = 0

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Q: Find a particular solution to the DE: y"+ 3y' – 4y = e* xe B. Yp = C. Yp = x²e* D. y, = xe-x E. None…

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Q: 15. As x increases uniformly at the rate of 0.002 feet per second, at what rate is the expression (1…

A: We have given that                     ( 1+x )3= f(x)      ,  then we have to find out value of dfdt…

Q: II P. Do Homework -Homework Chapter 4- part 1-Google Chrome…

A: Given query is to find the point where slope of tangent to the curve is zero.

Q: A hole of radius 1 inch is drilled through the center of a spherical wooden ball of radius 3 nches.…

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Q: Write the augmented matrix for the system of linear equations. 6x +y+6z = 8 3x- 7y-z = 6 x- 4y - 5z…

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Q: 2. Let f(x) = vVI(2 – x). Use the local linear approximation of f(x) at xo V0.99 (1.01)². 1 to…

A: Explained below

Q: Find curl (9z i+ 10xj+ 2y k). curl (9z i+ 10x j + 2y k) = ( i Di + ( i j+ ( i )k

A: We have to find the curl

Q: Find volume of the solid obtained by rotating the bounded region determined by curves y = In x, y =…

A: We have to calculate volume of solid obtained by rotating the region bounded by y=lnx, y=0 and x=2.…

Q: 1. The set of 2 x 2 matrices with real number entries, denoted M2(R) : a, b, c, d e R}, is a vector…

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Q: Find the inverse Laplace transform: 1 L-1 Is(s? + 1))

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Q: Use the Direct Comparison Test to determine the convergence or divergence of the series. 00 sin“(n)…

A: We have to find the convergence of series

Q: 3) Find the derivative Of S> Sin (xy) + e' v#5

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Q: 8 Evaluate for (3x² -7x+4

A: We have to use the concept of derivatives

Q: 1 mile = 5280 feet I km = 1000m %3D %3D 1m = 100 cm %3D 1L = 1000 ml 1 Calorie = 4184 joules 1…

A: Follow step 2

Q: Suppose that f is integrable on [-4, 7]. If the average value of f on the interval [-4,7] is 4.25,…

A: Given: Average value of f(x) on the interval [-4, 7] is 4.25 The formula for average value of f(x)…

Q: Evaluate the integral. 3-/4 5 sec e tan e de

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Q: 4. Evaluate lim (cos r)/". エ→0

A: we want to find the limit limx→0 ( cosx )1x2

Q: Consider the following vector field. F(x, y, z) = xy²z²1 + x²yz²j + x?y²zk (a) Find the curl of the…

A: div F = i∂∂x+j∂∂y+k∂∂zF(x,y,z) curl F = ∇×F