Find the slope of the tangent line to the curve 3 - 2x² + xy + y² I at the point (4, 1). - 27

Q: dr 3 - 4r - r2

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Q: Show that the average value of sin^2t over [0,2pi] is equal to 1/2. Without further calculation…

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Q: 22) A- Find the distance between the line (y=x+3) and center of circle (x²+y²-2x=0). B- Using…

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Q: Given x + y³ - 100y a.) Find all values of y that correspond to x = 7. Separate your answers by…

A: The equation is given by x+y3-100y=7                         ..........(1) To evaluate: (a) All…

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Q: Find div F and curl F if F(x, y, z) = x¹i − 6j + yzk. - div F= 7x + y curl F zi X

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Q: Find the vector v whose initial and terminal points are given below. (5.5,2.1), (9.5, 6.1)

A: Recall: The vector v with initial point (x1,y1) and terminal point (x2,y2) is, v=x2-x1, y2-y1 We…

Q: 7. Evaluate I = S ads, where S is the part of the plane x+y+z = a lying in the first octant.

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Q: If y = f(x), f'(x), (f(x+h)-f(x)) and slope of the tangent to the curve of f(x), h lim h→0 they all…

A: if y = f(x) Then,  By first principle of derivative

Q: 2) Determine as derivadas parciais de 1ª ordem das funções z=2e² sen(x) P(1,5). (valor: 1,0) no…

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Q: lim-(In(5n³-n+1)-in(7n³n+1)) 3 3

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Q: Let f(x)= I Determine f'(x). sin² (³+1) dt, x= [1,1].

A: Given: f(x)=∫-xx2sin2(t3+1)dt

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Q: Calculus

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Q: The equation of the tangent plane to the parametric surface x = u, y = v², z = uv at the point where…

A: This question can be solved using the concept of finding the tangent plane when the parametric…

Q: Find the general solution : (3x + 2y + 4) dx + (3x + 2y - 3) dy = 0

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Q: nsider the function f(x) = 6√√x +9 on the interval [1, 8]. Find the average or mean slope of the…

A: We have to solve the question for finding the slope

Q: potential

A: Please refer to the image below

Q: Q1) B- IF f(x)=√4-x, g(x)=x², Find : fog(x) draw them & determine (domain ,range). 9 gof(x),Then

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Q: Find the Taylor series generated by f at x=a. f(x) = 5x , a = 7

A: We have to find Taylor series of f(x) =5x about x=7. Let us see first what is Taylor series…

Q: Use the given function and the given interval to complete parts a and b. f(x) = 2x³ - 36x² + 192x on…

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Q: Find the average rate of change of the function over the given interval. f(t) = 2t² - 5, [3, 3.1]…

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Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

A: The objective of the question is determine the second solution of the given differential equation.

Q: Find the general solution of the given differential equation, and use it to determine how solutions…

A: Given Equation 8y'+y=8t2y'+18y=t2 Comparing with standard form y'+Py=Q P=18Q=t2

Q: Use a Maclaurin series in this table to obtain the Maclaurin series for the given function. 4x -…

A: we use the maclaurin series of sin x to find the maclaurin series of the given function

Q: In this problem, p is in dollars and x is the number of units. The demand function for a certain…

A: We know at equilibrium point demand function and supply function gives equal value.

Q: Newton's law of cooling states that the temperature of an object changes at a rate proportional to…

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Q: Estimate the area under the graph of f(x) = rectangles and right endpoints. Rn = Repeat the…

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Q: Iƒ F(t) =î+tj+t²k and G(t) = tî+e¹+3k, then find (F × G)(t) at t = 0. 0 Ok O î+ ĵ + k o î+î

A: Topic- Cross Product of vectors

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Q: Determine which of the following power series is equal to the function f(x) = -V2<<√2 0 0 n=0 IM IM…

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Q: Explain why if a runner completes a 6.2-mi race in 33 min, then he must have been running at exactly…

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Q: √ √x dx W|N 3 x2 + N/W N/W + C + C 2/3 + C

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Q: Question Find the change in volume dV if a circular cylinder with radius r = 8 changes height from 7…

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Q: 8] n=1 1 n√n +1

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Q: 2. Let f(x) = 2x²-3x+1 ,x 0.5 Determine constants A and B such that is continuous for all values of…

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Q: Find the area, A, between the curves y = In x and y = In 2x from x = 1 to x = 2. The area is A =…

A: The region is bounded by the curves y=ln x and y=ln2x from x=1 to x=2

Q: Find the total area of the shaded region. 1.5- 1- 0.5- 0 y x=12y³ 6 x=12y² (12,1) 12 18

A: The equation of the curves are: x = 12y3 x = 12y2 The graph of the curves is To evaluate: The area…

Q: Find the vertex, focus, and directrix of the parabola. y² + 2y + 16x + 33 = 0 (x, y) = vertex focus…

A: The given equation of parabola is:             y2+2y+16x+33=0⇒ y2+2y+1+16x+32=0⇒…

Q: Classify the given differential equation according to its type, order, degree, and linearity. (+)*…

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Q: Differentiate the function. Then find an equation of the tangent line at the indicated point on the…

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Q: sinx cosx 4 + sin4 x dx

A: The given integral is sinx cosx/(4+sin4x).

Q: Use implicit differentiation to find dy dx x3 + y = 15xy || dy dx

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Q: In a chemical reaction, one unit of compound Y and one unit of compound Z are converted into a…

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Q: Find the domain of the vector-valued function given below. r(t) = √√16-t²i+ 1 t+6 j+(t−4)k

A: We have to find the domain of the vector-valued function rt = 16-t2i + 1t+6j + t-4k

Q: If the period T is note equal to 27 but T=2L then f(x) = a + an bn Σ(ancosx + b₂ sin x) n=1 1 2L ao…

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Q: Use the definition of Taylor series to find the Taylor series, centered at c, for the function. f(x)…

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Q: the power series ∞ (7-2x)" Consider f(x) = Σ function. 6n n=1 as a a. Find the interval of…

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Q: Let Ln denote the left endpoint sum using n subintervals and let Rn denote the corresponding right…

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Q: Use Divergence Theorem to evaluate SF. Nds and find the outward flux of F(x,y,z) = xi+y²j−zk through…

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