Find parametric equations for the tangent line to the curve r(t) = (t² +e²t)i + (2+e¯³)j + (t³ − 3t+2) k at the point (132)

Q: 2 2 [² F(x) dx = [² f O True O False f(t) dt.

A: ∫02f(x)dx=∫02f(t)dt

Q: Use the Fundamental Theorem of Calculus to evaluate (if it exists) 2π −3 csc²(x) dx. π If the…

A:

Q: (a) (i) Prove from the definition of differentiability that the function x+3 a-2 is differentiable…

A: as per guidelines we are supposed to answer first question only.

Q: Suppose the region on the left in the figure (with blue shading) has area is 21, and the region on…

A: Here 2 regions are given. First region has area of 21 and other have area of 7.

Q: (4) Switch the order of integration for the double integrals below from dydz to drdy, or vice versa.…

A: Here we have to change the order of the integration.

Q: Set up the definite integral that is needed to find the area bounded between f(x) = 10x - x² and…

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Q: 2 S.S.x'y dydx x²y³ 0 0

A: ∫01∫02x2y3dydx

Q: Find the linearization of the function f(x, y) = x√√y at the point (5, 49). L(x, y) =

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Q: . 1. Determine à ☎ given thata = (2,−7) and b = (−3, 6) a) -36 b) -48 2. 3(2-3) -2( - 5u) -47…

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Q: Set up the definite integral that is needed to find the area of the region bounded by the curve y =…

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Q: use the parameter to write eah rectngular equation as a pair of parametric equation   y= -x^2/4 +…

A: use the parameter to write eah rectngular equation as a pair of parametric equation

Q: Sketch the graph of f and use your sketch to find the absolute and local maximum and minimum values…

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Q: For the function f, given below, find the antiderivative F that satisfies F(1) = 1. f(x)=x5-2x³+4…

A: fx=x5-2x-3+4

Q: Evaluate the iterated integral by converting to polar coordinates. 6*6*²= 0 T x² + y² dy dx dr de =

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Q: ndicate whether the statement is true or false. 1. The quotient rule can be used to differentiate a…

A: 1. True 2. False  [ power rule works with any real coefficient ]  3. False

Q: 9. Determine the polar coordinates of a point which maps to the same position as the polar point…

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Q: Convert the point (x, y, z) = ( − 4, 1, − 1) to spherical coordinates. Give answers as positive…

A: The cartesian coordinate is given by x, y, z = -4, 1,-1 To evaluate: The spherical polar coordinate…

Q: Find the limit. lim (x, y) -(1, 1) 00 -In 2 In 2 O No limit +V xy

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

Q: 19

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Q: converges or diverges. α) by apply the Limit Comparison Test to determine whether the given series Σ…

A: As per company guidelines only one question is allowed to answer for multiple question posted.…

Q: Find the curvature of the function y = ln (5x) at x = 2. Find the radius of curvature at x = 2.

A: As per guidelines we can solve only first question if multiple questions are posted. Please repost…

Q: Estimate the area between the curves y=1.5x and y=0.75x^2. Use a graphing calculator. Answer:

A: We have to estimate the area between curves.

Q: find derivative of  X3 – y3 + x2y6 = 9

A:

Q: Find the linearization of the function f(x, y) = √² L(x, y) = = x² y² at the point (3,5). Use the…

A: f(x,y)=43-x2-y2   at the point (3,5)

Q: A price ceiling is given along with demand and supply​ functions, where D(x) is the​ price, in…

A: To solve this problem, we need to compare the equilibrium point with the price ceiling.   Given that…

Q: 3. a. Find the MacLaurin polynomial with 5 nonzero terms for f(x)=sinx. b. Using (a), find the…

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Q: Find an equation in spherical coordinates for the rectangular equation x² + y² + z² - 5z = 0 Do not…

A: Geometry As per guidelines, at a time only one question can be answered. Please repost other…

Q: Find the derivative of : yo √√x ²³² +1 (x+3) * (x-1)/3

A: given  y=x2+1(x+3)x(x-1)13formula used is (i)  lnxn=nlnx(ii)  lnab=lna-lnb(iii)  lna.b=lna+lnb(iv)…

Q: Find a function f(n) that identifies the nth term an of the following recursively defined sequences,…

A: The Answer is in step2.

Q: The graph of a continuous function f is shown in the figure below. Arrange the following quantities…

A: .

Q: Find the length of the curve. r(t) = t² i + 9tj + 4ť³/2k, 1≤t≤4

A: Given vector function is: r(t)=t2i+9tj+4t3/2k We have to find length of curve for the interval [1,4]

Q: Find f such that f'(x) = 5x² + 9x-3 and f(0) = 8. f(x) =

A: Given that f'x=5x2+9x-3 and f0=8. We have to find the function fx.

Q: use the Alternating Series Test to determine if the series converges. If the Alternating Series Test…

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Q: The graph of g consists of two straight lines and a semicircle. Evaluate each integral by…

A: It is the area from 10 to 30 which is semicircle with radius r = 10 area of semicircle…

Q: Evaluate the limit lim Σ 1. 1-100 n lim Σ 1-100 i=1

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

Q: Let F(x) = 1X-11, Sketch the graph of F(X). Then answer the following: IS F(x) continuous at x = 1 ?…

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Q: Find the first partial derivatives of f(x, y, z) af A. (5,5,-2) = B. of (5,5,-2) მყ = C. (5,5,-2) =…

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Q: Describe the surface. x2 − y2 = 5 Write an equation for the cross section at  z = −5  using x and…

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Q: Because of material shortages, it is increasingly expensive to produce 6.2L diesel engines. In fact,…

A: To find the inflection point of the function P(x) = -x3 + 30x2 + 10x - 52, where 0 ≤x ≤20 to…

Q: Find all the first order partial derivatives for the following function. f(x, y) ਨਾਲ ਹ 11 11 11…

A: Given: f(x,y)=1x2+y2 We are required to find: ∂f∂x and ∂f∂y

Q: . For function, find (a) the critical values; (b) the largest open intervals where the function…

A: Application of differentiation

Q: 2T * sin(²) cose dr de 0

A: To evaluate the following integral. ∫02π∫23sinr2 cos θ  dr dθ

Q: Explain why the function is differentiable at the given point. f(x, y) = x³y², (-2, 2) The partial…

A: .

Q: Find the partial derivatives of the function дw Ər δω Əs δω Ət || || w = √r²+7s² + 6t²

A: The given function is w=sqrt(r2+7s2+6t2).

Q: 11. For the following initial value problem, compute the first four approximations U₁, U₂, U3, U4…

A: The solution is shown in step-2

Q: Demand for apartments in a certain town is D(x)=1480−3x​,and the supply is S(x)=500+11x​, where x…

A: To find the equilibrium point, we need to find the value of x for which demand equals supply, i.e.,…

Q: Determine the absolute maximum value of f(x) = sin(x) - cos²(x) =

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Q: What does L'a a(t) dt, represent if a(t) is acceleration in km/hr² and t is time in hours? This…

A: in the given form of integration a(t) represent acceleration which also can be written as dvdt.

Q: After t seconds the displacement, s(t), of a particle moving rightwards along the x-axis is given…

A: The average Velocity equals to the average rate of change of displacement The average rate of change…

Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an…

A: