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Q: 4. f(t) = teatcosbt

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Q: Encounter the critical points of f(x, y) = 16x3 - 9y2 - 36x2 - 12y + 6x - 27 and then denote each…

A: To find out the critical points and denote it's nature.

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Q: , can you draw the graphs clearer? or maybe in digital?

A: Given problem:- Draw the figure which represents area bounded by given curves 1) y= x2+2 , x=2 and…

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Q: A particle moves with position function s = t4 - 4t3 - 8t2 + 25t, t2 0 (a) At what time does the…

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Q: S tan“ x sec“ x dx

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

Q: Find the exact length of the curve. Ex372, 0sxs 4 y =

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Q: 6. What type of discontinuity at x = 1 is in the function f(x) =? (A) infinite discontinuity (C)…

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Q: Write a in the form a = a7T+anN at the given value of t without finding T and N. r(t) = (- 2t + 3)i…

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Q: 1) Find the hundredth derivative of p (x) = (x+ x³ + x")1º (1 + x²)!' (x³ + x³ + x7). Justify your…

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Q: Find the slope of the tangent line to the curve - 2x2 + 3xy + 4y° 3 242 at the point (- 1, 4).

A: Solve the following

Q: 32 Suppose that f(x, y) = x°y². The directional derivative of f(x, y) in the directional (1, 2) and…

A: Given problem:- Suppose that f(x, y) = x3 y2 . The directional derivative of f(x, y) in the…

Q: find two real numbers whose difference is 24 d whose product is minimum, we can find th inimum value…

A: We will find the function.

Q: Problem 12 Find the following indefinite integrals (a) S(9x² + 8x +3)dr (b) S(x-4 – 9/I)dr (c)…

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Q: Find each function value and limit. Use -∞ or co where appropriate. 7x* - 14x2 f(x) = 8x° +4 (A) f(-…

A: topic- functions and limits

Q: Refer to the figure below to find the limit lim f(x). X - 00 3.5- 2.5- 1.5- 1- 0.5- 2.

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Q: The Laplace transform of ,-2r ,3(1-t) dt e is Select one: 1 (s + 3)(s – 2) 1 (s + 3)(s + 2) 1 (s –…

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Q: Matching Type. Match the functions in Column A with their corresponding antiderivatives in Column B.…

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Q: Given the triangle 13 find the length of side x using the Law of Cosines. Round your final answer…

A: This question is related to Triangles, we will solve it using given information.

Q: Write a in the form a = a-T+aNN at the given value of t without finding T and N. 3 (5 e'V5)i+…

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Q: QV Optimize the function Z = xị + xị Subject to: x1 + x2 = 4 x1, x2, 20 Using Lagrange multipliers.

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Q: Find the velocity and acceleration vectors in terms of u, and ue en r=6 sin t and 0= 9t

A: The velocity is given by            v = r' ur +rθ' uθandThe accerleration is given by        a =r"-r…

Q: 12. Find the maximum and minimum values of each function. Graph each function. а. у %3D е* + 2 b. у…

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Q: Express the vector - 6i + 6j + 7k as a product of its length and direction. - 6i + 6j + 7k…

A: For a given vector v→, length of the vector is denoted by v→  and direction vector is obtained by…

Q: 4. Determine the equation of the plane passing through the point (1, –4, 3) and parallel to x – y…

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Q: Directions: Determine the reasons of the following statement In the given figure, if EF GH, then EG=…

A: We want to identify the steps.

Q: To-42 5-2X-3 (6z) odz dy oe aly de

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Q: Let -1 <r< 1, the series r na" is the power series representation of the n-1 function

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Q: The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at x = x =…

A: P(x) has roots of multiplicity 2 at x=1 so (x-1)2 is a factor of P(x).  P(x) has roots of…

Q: Determine the antiderivatives of the following functions: 1. V1-4x² dx 12 2. 1+9x² dx 3. 4+(x-3)² dx

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Q: Evaluate the limit x2+ 19x-48 lim x²+9x+112 X- - 16 X a. 13 23 O b. 19 23 O C. 00 O d. None of…

A: The detailed solution is given below Thank you

Q: 2. A boat is being pulled into a dock by a rope attached to it and passing through a pulley on the…

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Q: Problem 9 Compute the derivatives of: (a) f(x)= e6z²+3z (b) g(x) = r°e² (c) h(x) = In(3r“ + 2x)

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Q: se' z = st. Solve for dz IV. Let w = x ln x + 2xyz + 5z°y, x = tan s + r, y =

A: Given problem:- Let w = xln(x3) + 2xyz + 5z3y, x = tan s + r, y = (set )/r, z = st Solve for partial…

Q: Find the volume oF the solid obtained by rotating about the Y- axis the region bounded by Y= x2 and…

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Q: 5. Let f(x) be the function f(x) = {* T*7 makes the function f(x) continuous for all real numbers.…

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Q: fi(x)-2• sin(x) -3- R 3- 5- 3.* 4. 4 2 -2

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Q: V. Let z be a function of r and y, and tan y2 + x2 = z*ey. Solve for dz dz and

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Q: y =1+6.x% Osrsl for Find the exact length of the curve

A: Length of the curve

Q: Test the given geometric series for convergence or divergence. If it converges, find its sum. 4 16…

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Q: olve the triangle. 95 a-6 b- 4 Select the correct choice below and, if necessary, fill in the answer…

A: Here is the solution

Q: 12 Consider the graph of the ellipse. which is drawn to scale. This ellipse has an eccentricity of…

A: Given query is to find the equation of the ellipse.

Q: n Apply the Integral Test to the series E n=1 n²+1

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Q: Find each limit. Use - o or ∞ when appropriate. 4x-4 f(x) = - (x- 4)? (A) lim f(x) (B) lim f(x) (C)…

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Q: I. Find the general solution of the following: dy 2x 1.- dx y dy 2. xy dx 3. dy = (6e3x+ 1)dx

A: We have to find the general solution.     According to our guidelines we can do only one question so…

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Q: Find an equation for the plane through the points (3, 4, 33), (2,1 -2), (0, 1, –1). The plane is

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Q: 1. lim (6x + 1)cotx

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Q: f'(x)= -+e²* +x°and f (1) = Find f(x) Given 5.

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