Choose the normal vector of the tangent plane to the surface defined by Z = e6x²+14xy-5y² at the point (3,-4,4). O -20 1949 82 194 - 1>

Q: A. Find the following limits. Answer four only. x-¹-1 i. ii. iii. lim- X-1 X-1 lim 4x-x² X-4 2-√√x…

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Q: 5 +1 Tsimplify denomina 7) (1+i) (1-1) = 4 the Following without using the de noctor Prove that

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Q: Use Gauss-Jordan elimination to solve the given system. 3x + 6y – 3z = −2 -2y + 3z = 1 6x + 6y + 3z…

A: Follow the procedure given below.

Q: given the surface revolution x^2+z^2-5y=0 find the equation of its generating curve in the yz-plane…

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Q: Consider the following function. f(x) = e3x² a = 0, n = 3, 0 ≤ x ≤ 0.1 (a) Approximate f by a Taylor…

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Q: Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule with n = 4. Compare…

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Q: find the distance between point (-1,1,3) and the plane 5x-5y+3z=25

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Q: Find all the zeros. Write the answer in exact form. q(x)=x²-₁ -7x+14x-6 If there is more than one…

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Q: Given the initial condition y(0) = 2, what i the particular solution of the equation √x - √ (x² +…

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Q: Given that f(x) = h(x) x5 f'(-1). Show your work. -, h(-1) = 4, and h' (-1) = 7 find

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Q: parametric

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Q: Q2/A Cylindrical tank with radius of (3 m) and height of (10 m) has initially filled with water. In…

A: Please see the below picture for detailed solution.

Q: Write an equation for the function graphed below -7 -6 y = -5 -4 -3 Get help: Video 5 4 3 2 1 -2 -3…

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Q: V. Provide up to the 5th degree Taylor Polynomial of the given function: f(x)= xex by about x=-1

A: Given :fx=xe-xx=-1

Q: 4. What are the values of A, B, C, and D so that 1 a. A = b. A = C. A = d. A = HALA00 B= C= B B 1 8'…

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Q: Find the indefinite integral using any method. (Use C for the constant of integration.) I'v 1 +…

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Q: Given that S." sin xdx = 2, find the average value of the sine function on the interval [0, π].…

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Q: What transformation is required to obtain the graph of the function f(x) = 7cosx from the graph of…

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Q: B. Solve one of the following inequalities. Write your answer as an interval or union of intervals.…

A: Please see the answer below.

Q: Find all the values of x such that the given series would converge. (x-8)" 8n n=1 The series is…

A: We will use ratio test.

Q: Consider the function on the interval (0, 2). f(x) = 2x + 4 sin(x) (a) Find the open intervals on…

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Q: Use L'Hopital's to determine the limit. lim Oo O1 ○ -1 enx ~|-1 as x approaches co

A: This question can be solved using the concept of L' Hopital's Rule and derivatives.

Q: Find the critical points of the given function. 1 a) f(x) = -√24/3+2¹/ +2-2/3

A: Since multiple questions are asked, I am answering first question

Q: LI) Prove that (3

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Q: 5. Solve for x² − x+6 x³ + 3x 1³ dx.

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Q: 1. Find the total area bounded by the curves y=x²-3x and y = x³ + x² −12x.

A: Given Graphs y=x2-3xy=x3+x2-12x First we find point of intersection of graphs…

Q: The vector v and it's initial point is given find terminal point v=, initial point (-7,-8)

A: In this question we have to find terminal point.

Q: prove that :: 2) (1+i) (1-1)² = 64

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Q: Sketch the region enclosed by the curves and find its area. Enter the exact answer. Area = y = 2x²y…

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Q: 2. A circular cylindrical hole is bored through a solid sphere, the axis of the hole is being a…

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Q: Let g(u) be a function such that f g(u) du = ln (1 + 8u²) + C. Evaluate fxg(x²) dx.

A: This question can be solved using the concept of integration by substitution and definite integrals.

Q: Use the method of reduction of order to find a second solution of the differential equation t²y"…

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Q: Given the function of two variables f(x, y)= ln (√x + y6) The partial derivative with respect to x…

A: using the partial derivative,

Q: Suppose that a particle moves along a straight line with velocity v(t) = 10 - 1t, where 0 ≤ t ≤ 5.5…

A: Given: v(t)=10 -t, 0≤t≤5.5

Q: 1.) Sand hole conical pile altitude always 1 4 of increasing when the 14 pouring from a the conical…

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Q: find the unit vector in the direction of u u=

A: find the unit vector in the direction of u u=<-4,-1,-3>

Q: A spherical raindrop evaporates at a rate proportional to its surface area with (positive) constant…

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Q: F(x)= -sqrt(4x+1)-2 This is the value of the function

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Q: Use logarithmic differentiation to find the derivative of y y = X X+7 OA. OB. O C. (3)√ 2 7 O D. X…

A: topic- differentiation properties of log used:log(ab)=blog(a)logab=log(a)-log(b)derivative formula…

Q: 3. Solve one of the following inequalities. Write your answer as an interval or union of intervals.…

A: This question is based on finding solution of inequality.

Q: Use integration by parts to find the indefinite integral. (Use C for the constant of integration.…

A: Note: ln(a×b)=ln(a)×ln(b)....(i) ln(an)=n×ln(an) ..........(ii)

Q: ΒΣ 3 Θέλη

A: 3.The given series ∑n=0∞3.12n

Q: c) x² + xy = 2x² +1. d) = 2² sin(3r) +2. d

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

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Q: Find the definite integral that will compute for the area of the region bounded by y = ex, y = 0, x…

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Q: Given that 0. ∞ n=0 x = 1 1 <- x to x = = Identify its interval of convergence. The series is…

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Q: Find the radius of convergence, R, and the interval of convergence, I, of the following series.

A: The given series: ∑n=2∞x+2n2n ln n

Q: (14 Find the derivative of the function 7 (^ Y = x²+3 15 x²-3

A: Find the derivative of the function  y= [(x2+3)/(x2-3)]5

Q: For the IVP, y'=f(x,y), y=yo, x=xo, iff and df/dy are continuous discontinous defined undefined then…

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Q: g(x) dx = (Simplify your answer.) 7 4g(x)dx= 2 (Simplify your answer.) 7 [g(x)-f(x)]dx = (Simplify…

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