ntinuous function, f (x), has a domain of [-6, 6] -6

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: Consider the following equations. f(x) = x5 + 3 %3D g(x) x + 3 %3D

A: The region is bounded by the graphs,  fx=x5+3 and gx=x+3

Q: tarts with 40 bacteria and grows at a

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Q: 4. Evaluate lim (cos r)/". エ→0

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

Q: At 10:17 a.m., you pass a police car at 55mph that is stopped on the freeway. You pass a second…

A: Here, note that the distance between two police cars is 39 miles and the time between them is…

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: A plane P, in R'is perpendicular to the vector n = (6, 2, 8), and contains the point (– 9, – 1, –…

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Q: Evaluate: L7 3sin13 edx 512 1001 1024 1001 O 1024 1001 512 1001

A: Solution of given question is written in below steps.

Q: u-3 15) If y= u+4 and u = 2/x+ 2, find when x = 7 dx %3D

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Q: d d Calculate ri(t) · r2(t)] and r:(t) x r2(t)] first by differentiating dt dt the product directly…

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Q: Determine the vector field of F. F(x, y) = 8i – 4j

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

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Q: if an open box is to be made using a square sheet of tin, 20 inches by 20 inches, by cutting a…

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Q: Find V x (V x F) if F(x, y, z) = 2xy j+ 6xyz k. %3D V × (V × F) =

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Q: Find the sum of the convergent series. 4 Σ n(n + 2) n = 1

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Q: II. Use the first fundamental theorem of calculus to find F'(x) .Write your final answer on the box.…

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Q: Find the antiderivative of f(x) = 2 csc2 a given that f () = 1. 4.

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Q: Find the minimum amount of tin sheet that can be made into a closed cylinder having a volume of 108…

A: In this question we have to find the minimum amount of tin sheet that can be made into a closed…

Q: It can be shown that the polar curve r = a sin(0) +b cos(0), where ab + 0, is a circle. Find the…

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Q: 3. If dt , find g'(2). 5. g(x) =

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Q: Describe the graph of the equation. r = - 13 i+ (1 – 12 )j + t k O It is a parabola in the plane x =…

A: Given; parametric equation    r=-13i+(1-t^2)j+tk

Q: 4proof that d sech u = dx - Sech u tanhu.du dx

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Q: sinex) sintpx) x

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Q: Draw a graph that does not pass through -8 and 8. Identify 3 points that is continuous at that…

A: Solve the following

Q: Sx³e*²dx 3. X°e

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Q: 11. Use the guideline in §4.4 to sketch the curve: f(x) = x² ln x. A). Domain, Symmetry, Asymptotes,…

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Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS. P(-2, 1, 0), Q(4, 5, 4),…

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Q: Find V (F x G), if F(x, y, z) = 11xi+j+13yk and G(x, y, z) = xi + yj – zk. %3D V. (F x G) =

A: Given,            Fx,y,z=11xi+j+13yk and Gx,y,z=xi+yj-zkTo find : ∇·F×G

Q: ||r(t) × r"(t)|| Use the formula k(t) to find k(t). 3 r(t) = 11 cos(4t)i+ 11 sin(4t)j+ tk K(t) =

A:

Q: Find the area of the shaded region 10x) = 8x - 2x - x, g0x) = 0

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Q: Find V · (V × F), if F(x, y, z) = 2e"*i+4xe"j – 4c*k. V · (V × F) =

A:

Q: valuate the indefinite integral. 7 dt (t + 1)?

A: Given query is to eveluate the integral.

Q: Find the fourier senes for the Periodic extension given below! te [o, 2] X (t) = -1 te [2,4]

A:

Q: Find div F and curl F if F(x, y, z) = xz°i+ 2y'x²j+ 2z²yk. %3D div F= curl F=

A:

Q: The height of a right circular cone is always three times the radius. Find the volume of the cone at…

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Q: Let f be a function admitting continuous second partial derivatives, about which it is known that:…

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Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) Y1…

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Q: r In x 2

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Q: 1 2 3 1+3* Use substitution to find the Taylor series at x= 0 of the function ... 1 What is the…

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Q: Find the value of the specified finite sum. Given ak = 3 and bk = 7, find (ak- 2bk). %3D k=1 k=1 k=1

A: We can find the specified finite sum as below.

Q: 3 (2). Consider the solid Q bounded by the surface of the equation y =x² + z? and the planes, zV3 =…

A: Here's the solution... please have a look at it.. Answer: option C

Q: initial deposit of $1,000 is placed in a savings account with an APY of 4.3% sume the interest rate…

A:

Q: 2. Let f(x) = VI(2 – x)². Use the local linear approximation of f(x) at ro = 1 to estimate V0.99…

A: f(x)=x2-x2The linear approximation of f(x) at x0=1

Q: 3x + 4y – 5z= - 8 4x + y- z= - 14 x- 3y + 3z = - 10

A: answer is in next step

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: 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: Using the laplace transformation formula, ∫ f(t) e^−st dt evaluate L[8t^2 e^-2t]

A: Laplace transform of the function f(x)Lf(t)=∫0∞e-stf(t)dt

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly.…

A: Here we have to use green's theorem.

Q: The fifth derivative of the function f(x) = 5x° is a constar False O True

A: Given query is to find statement is true or false.

Q: A concert promoter needs to make $81,000 from the sale of 1800 tickets. The promoter charges $40 for…

A: x+y=1800x= number of $40 ticketsy= number of $70 tickets