Use the graph of f (x): = Enter the exact answer. 1/1/00 below to find a number & such that |ƒ (x) - 0.5| < 0.1 whenever 0 < x − 2| < 8. 8 = Number 8 y 1 0.6- 0.5 0.4 0 2 X

Q: Let the line PQ pass through the points P = (-4,-4, -6) and Q = (-2, 1, - 16). The line will pass…

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Q: Find the cross product u x 7 where u = 2i -3j +k and = (7, - 3, 4). ü xü= Check Answer

A: We have u→=2i-3j+kor u→=2, -3, 1Alsov→=7, -3, 4

Q: 2. Solve the differential equation dx for y = f(x) with the initial condition y(0) = 2.

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Q: Compute ₁₁x dx using the concept of integral as limit of sums.

A: The given integral is ∫-11xdx use the properties of integral: ∫abf(x)dx=∫acf(x)dx+∫cbf(x)dx, where…

Q: 8. What is the domain and range of the following relation? y=x²-2x-3 y 5 8 X

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Q: (a) Consider the power series Show that B(x) converges for all x. B(x) = Σ n=0 (-1)η 2η 22n (n!) ²

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Q: Evaluate the definite integral (3625 - 24) dz using Part 1 of the Fundamental Theorem of Calculus.…

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Q: = Set up the definite integral required to find the area of the region between the graph of y y = 2x…

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Q: 2 √9x²-16 x² dx

A: We will use substitute method to solve the integration

Q: Find a vector with initial point (4, -4,0) and terminal point (7, -14, - 10). Then find a unit…

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

Q: Find the arc length (s) of the curve r(t) = (3t, 2 sin(2t), 2 cos (2t)) for -4 < t 5 S = Check…

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Q: √x+9 at x = 0. Write your answer in the form a+bx+cnx" n=2 where a, b, and each cn are constants.…

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Q: Let r(t) = (-5t5 - 3, 4e-4t, 5 sin(2t)) - Find the unit tangent vector T (t) at the point t = 0.…

A: Given vector  r(t)→=&lt;-5t5-3,4e-4t,-5sin(2t)&gt;

Q: Find the mass of the surface lamina S of density p. S: z = √₂²x² - y², p(x, y, z) = kz ka+n 2 X

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Q: у=ех

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Q: c) 2x²8x + 4x³ - 4

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Q: Find the work required to move an object in the force field F = (x,2) along the straight line from…

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Q: Find the point at which the line y(t) z(t) = 2 + 4t -6-8t intersects the yz plane. 6-7t

A: The line x(t)=2+4t, y(t)=-6-8t, z(t)=6-7t intersect yz plane Note:    Multiple questions are given,…

Q: Evaluate the Integral using the following values. [°x³ dx = 260, [°x dx = 10, [°dx = 2 [°(22-7x-x²)…

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Q: Evaluate the definite Integral. Use a graphing utility to verify your result. [² (u - ) du

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Q: ㅠ 10. fž sint p cos3 p dp 2

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Q: 2 area of region .25 and 2 Use horizontal strips to find the area, that is, integrate with respect…

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Q: Find the curvature of the curve r(t) = (5 + 4t, 4 - 4t, 1 - 3t) at the point t = -6. Check Answer

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Q: Which function has Maclaurin series (-1)"2""? n:o OAI OB 8. 2/7/2 Oc O D. TIZE D.E. 2

A: The given series: ∑n=0∞-1n2nxn

Q: 4. Which of the following is f(x) = x² the parent function for? a) f(x) = x³ + 2x²-x+ 13. b)…

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Q: Find the directional derivative of f at the given point in the direction indicated by angle f(x,y)…

A: Given function is: f(x,y)=excosy We have to find the directional derivative at the point (0,0) in…

Q: Let P be the set of positive real numbers. One can show that the set P³ = {(x, y, z)|x, y, z € P}…

A: The objective of the question is determine the vector .

Q: Consider the equations of two planes. x + y + z = 0, 8x - y + z-5=0 (a) Determine whether the planes…

A: This question can be solved using the concept of angle between two planes.

Q: 2.fe-2y dy

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Q: = Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep…

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Q: (a) Find an affine change of coordinates that takes the unit square with vertices in the uv-plane to…

A: (a) The vertices of uv-plane is given as , P*=0,0 , Q*=1,0 , R*=0,1 , S*=1,1 and the vertices of…

Q: Using calculus, find the absolute maximum and absolute minimum of the function f(x) = 7x² − 14x + 4…

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Q: ✓ ["1 [™ f(a)da - [* f(x)dx = - Sª f(x)dx and b where a = If what are the bounds of integration for…

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Q: 3. Find the vertex, focus, and equation of the directrix for the conic given by (x + 1)² = -20(y -…

A: We have to find focus, vertex and equation of directrix.

Q: Given the differential equation dy dx = y³ x ex² 9. Find a solution that satisfies the initial…

A: Differential equation: dydx=y3xex2

Q: Please show your answers to at least 4 decimal places. Find the directional derivative of the…

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Q: Find two positive numbers with product 625 and whose sum is a minimum. Enter your answers in…

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Q: Which of the following functions will have a dashed line for the graph? y ≤ 4x^2 + 1 y = 4x^2 + 1…

A: Question : Which of the following functions will have a dashed line for the graph? 1. y ≤ 4x^2 + 1…

Q: Find the volume of the region bounded by z = x²,0 ≤ x ≤ 5, and the planes y = 0, y = 2, and z = 0.…

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Q: Find the mass of the two dimensional object that is centered at the origin. A plate of radius 10…

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Q: Find 2 -1 (3x³ + 7x¹) dx

A: Here we have to solve definite integral

Q: 5) each k=1 (- series, find the sum. k - 1 6) k=1 +1) (k+2)

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: Find the curvature of the curve r(t) = (-1-4t, 2-t, 4 - 4t) at the point t = - 1. Check Answer

A: We know that curvature of a curve is given as: k=||r'(t)×r''(t)||||r'(t)||3

Q: 5 Suppose f(x) dx = 4 and g(x) dx = 3. 96 -3 -3 5 Evaluate (3 f(x) + 2 g(x)) dr. -3 Remember to…

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Q: 17.The volume of a parallelepiped is given by the following formula: a. c.(axb) Calculate the volume…

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Q: e) 9x³ + 6x² + 18x + 12

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Q: 191. f(x) = x³ + 1

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Q: The regions A, B, and C in the figure below are bounded by the graph of the function f and the…

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Q: 16

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Q: Find the area of a triangle PQR, where P = (-1,-1, 1), Q = (4, -3, -6), and R = (1, -6, -3) Check…

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