||r(t) × r"(t)|| ||r(t)||° Use the formula k(t) to find k(t). r(t) = t'i + tốj K(t) =

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Q: L xe* xe2x dx хе

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Q: a) Determine the intersection points. b) Draw a sketch of the graph. c) Find the area of the region…

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: First we will draw graph for function.

Q: ) Find p(3). ) Find p(13). =) Find p(13)-p(3). p(13)-p(3) 1) Find and interpret this result. 13-3 -)…

A: Given query is to find the value of the function at indicated points.

Q: Let f(x, y, z) = x*y+ z* and x = st², y = st, and z = s²t. (a) Calculate the primary derivatives se…

A: Given,  f(x,y,z)=x4y+z4x=st2, y=st, z=s2t

Q: It is desired to build a rectangular box of maximum volume such that the sum of the length of the…

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

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Q: 2. Show that if x and y are two vectors, then

A: Replace x→ by u→ & y→ by v→     Graphing software do not accept label x, y To show: u - v ≤u±v≤u…

Q: -2000x has the marginal-demand function D'x)= where Dx) is the number of units sold at x dollars per…

A: First we'll integrate and the we'll put the given value. So i am providing my handwritten notes…

Q: A light on the ground 100 feet from a building is shining at a 6-foot tall man walking away from the…

A: A light on the ground 100 feet from a building is shining at a 6-foot tall man walking away from the…

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

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Q: 2+ 12 40. Find all local extreme values of f(a) The FIRST local extreme value, moving from left to…

A: Find out the maxima and minima.

Q: A particle is moving with acceleration a(t) = 18t + 4. its position at timet = 0 is s(0) = 6 and its…

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

Q: - In(a°y*) + x2 Consider z as a function of the variables x, y which is denoted by z and let P(1,-1)…

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Q: Given the function below f(x) = V-80x + 144 Find the equation of the tangent line to the graph of…

A: Given :

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

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Q: If a rock is dropped from a height of 193 ft, its poistiont seconds after it is dropped until it…

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Q: If the roots of a homogeneous DE with constant coefficients were: m1= 0, m2 = 3 & m3 = 2 ± 3i , what…

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Q: Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat…

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Q: Consider the change of variable u = xy and v = 3y + 2x and the integral 2.r + 3y – 6 =0 - ||. (2r²y…

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Q: 2.x4 + x3 x4 xp-

A: Given query is to find the value of the integral.

Q: Let fa)=S(-5-x2 + 23x +19 f Xチー6 if X= -6 calculate the following limits. ENter DNE if the liniit…

A: l

Q: Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is…

A: We can solve as follows

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

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Q: The ellipse shown below has parametric equations x(t) = A cos t, y(t) = B sin t, 0 <t< 27.

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Q: The motion of a point on the circumference of a rolling wheel of radius 3 feet is described by the…

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Q: The function f(x) = 2+ 6x + 150x- has one local minimum and one local maximum. This function has a…

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Q: Consider the function f(x) on the interval [1, 11]. Find the average or mean slope of the function…

A: Given,  f(x)=1x

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

A: Explained below

Q: If the amount of bacteria in a culture at any time increases at a rate proportional to the amount of…

A: answer is in next step

Q: Find V. (V x F), if F(x, y, z) = 3e"i+ 7xe"j – 3ek. V.(V × F)

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Q: Solve the following differential equation (6х' — у +3)dx + (Зу* — х- 2)dy

A: Here, i am providing the handwritten solution

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

A: Given query is to eveluate the integral.

Q: a) Graph the function f(x) = 2x -5x+3 b) Draw a tangent line to the graph at the point whose…

A: Given the function is  f(x) = 2x2-5x+3

Q: The table gives the U.S. population to the nearest million for selected years from 1950 and…

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Q: Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is…

A: Use limit concept

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

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Q: Write the equation of the trigonometric graph. try sin x )+ 5 4. 2 31 57 37 2 -2 -3 -4 || 3. 1.

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Q: Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of…

A: We have to use the concept of derivatives

Q: Find V · (F × G), if F(x, y, z) = 2xi+j+14yk and G(x, y, z) = xi+ yj – zk. %3D - V · (F × G) = %3D

A: To solve the following problem

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A: Solve the following

Q: -dA dV dp 1. It shows that the behavior of fluid is A From the equation stated, show the formula +…

A: Here we have taken constant acceleration d2sdt2=dVdt To find the value of particular solution s(t)…

Q: The slope of the tangent line is

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Q: The matrix associated with the solution to a system of linear equations in x, y, and z is given.…

A: Solve the following

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

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Q: the 1. For f(x) = r8/3 - 4x5/3, find a). the domain and f', b). f" (simplify f"), %3D c). the…

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Q: Find curl (4z i+ 5x j+ 8y k). curl(4z i+ 5x j+ 8y k) = ( )i +( i j+( i )k

A: To Find : curl(4z i + 5x j +8y k)   Note that : If F=〈P,Q,R〉 is a vector field in ℝ3, and Px,Qy, and…