Use the graph of f(x) = below to find a number & such that f(z)-0.5| < 0.1 whenever 0 < |z-2|< 8. y 1- 0.6 0.5 0.4

Q: Solve the differential equation for y: t-³y' (t) = 1.

A: use separtion of variable and integral

Q: [5] Complete a first derivative test for the function shown below. Include local minima and maxima.…

A: The given function is:f(x)=(1-x)2x2-12

Q: 10. Find the horizontal and vertical asymptotes of the curve. 2x² +1 (a) y=- √x*-4 2x²+x-1 x²+x-2…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Inverse Laplace transform, x-1| (8²+1) 1 (s²+1)(s-3) Select one: O True O False cos(t) 10 3sin(t) 10…

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Q: Find the exact length of the curve. x = 8 + 12t2,    y = 3 + 8t3,    0 ≤ t ≤ 2

A: Given that:   x = 8+12t2 and  y = 3+8t3 , 0&lt;=t&lt;=2. Find the exact length of the curve.   Here…

Q: What is the standard form equation of an ellipse that has vertices (-2, -18) and (-2, 8) and foci…

A: Here is the solution

Q: Evaluate the integral. 16 4 6 sinh (Vx) √x dx

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Q: Supply the missing constant, k, so that the resulting trinomial is a perfect square. Then factor the…

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Q: convergent serie 12) Find the sum of each 2 A) / + = + ( ² ) ² + ( ² ) ³ + ( ²1 ) 4 + ... ( - )^² +…

A: Let's find sum of given series.

Q: 8) The Bernoulli's equation += dz NIH 2 218 I can be reduced to which linear differential equation?…

A: Ode

Q: Solve the problem. Let A = O -5 Define a transformation T: R³ -> R² by T(x) = Ax. Find T(u), the…

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Q: 17x 9 + 14x5-6x³

A: The given equation is; 17x9+14x5-6x3

Q: (c) Use the graph to find T₂. T₂ = 27 x How does it compare with I? T₂ <✔✔ I (d) For any value of n,…

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Q: 7) What value of N(x, y) will make the differential equation (3r2y +422)dr + N(x,y)dy = 0 exact? a)…

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Q: Find the average value of f on [0, 24]. YA 2 0 6 12 18 X

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Q: Evaluate the following integrals (cont'd) (c) S dx (9-x²)3/2 dx

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Q: (a) Eliminate the parameter and write the rectangular equation (b) Sketch the curve represented by…

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Q: 16) Let f(m)-0 be the auxiliary equation of f(D)y=0 with solution set equal to (-1,0,0,2), then…

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Q: Find the arc length of the graph of y = (²+2)³/2 from x=2 to x = 8. In this case the answer is a…

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Q: 1: Find dy if y³-4y² = x³ + 3x². dx 2: Find DPP 7 DERIVATIVE dy dx if sin y² - cos x² = cos y² + sin…

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Q: Explain the relationship between a function and the derivative by providing an example.

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Q: Differential equation: Families of Curves * w/ complete solution and sketch. Obtain the…

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Q: 2 2 Find the area of the surface cut from the paraboloid x² + y² + z = 0 by the plane z = -20.

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Q: Evaluate the integral: flatan (be) sec² (be)]de where a and b are positive constants. If you like…

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Q: Find the Taylor polynomial of order 3 centered at 0. f(x) = ex 12 2 1 3 OA. P3(x)=1-x+ O B. P3(x) =…

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Q: Consider the functions y = (x - 2)² +3. 13. a. Find the inverse of the function. b. Find f-¹(-4). If…

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Q: On graph (A) draw a function that is continuous on [-2, 2]. On graph (B) draw a function that has an…

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Q: List each of the mistakes in the following calculations: d a) [(cos z)] = x(cos x)²-1 da d b) [(cos…

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Q: Textbook Find c> 0 such that the area of the region enclosed by the parabolas y = r² c² and y = c² -…

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

Q: Graph the ellipse given below by dragging the center, vertex, and co-vertex points to the correct…

A: To graph the ellipse given below with the center, vertex, and co‐vertex to the correct…

Q: Find d da [e³²2²] dx 6xe ³x² e ³x² 6x e ³x² 6x (eª) (e³²²) (3x²) (6x)

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Q: Graph the hyperbola given below using the transverse axis, the center, the vertices, and the…

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Q: 1) Write the Taylor Series for f(x) = x³ about x = -2 as Сп (x+2) ". n=o First 5 terms.

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Q: 5) 14. If an object is moving in space with a velocity function of v(t)= t²-2t -8 where t is in…

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Q: To measure cover the height of the cloud worker shines a spotlight upward at an angle 75° from the…

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Q: Identify any vertical and horizontal asymptotes for the following graph. Write a limit statement to…

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Q: (8) Compute 100 [ f(x) dz 3 f(x) dx where f(x) = √9-x² ³x+3 if -3<x<0 if 0<x< 50 -162 if 50 ≤ x ≤…

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Q: 13) Let f(x) = 4+4x x Compute f(x), f'(x), f'(x), f'''(x), f(iv) (x), f(v) (x) S f(), f'(), f), F"…

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Q: Find the following using the table below. x 1 2 3 4 f(x) 2 1 4 f'(x) 3 1 g(x) 4 3 2 1 g'(x) 1 3 2 4…

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Q: 13. Find ƒ. (1)ƒ'(x)=x² + 3√x (2) f(t)=2cost+sec²t,-/2 <t</2,ƒ(π/3)=4; (3)ƒ*(x) = 6x+sinx.

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Q: Consider the solid obtained by rotating the region bounded by the given curves about the x-axis. 3…

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Q: Evaluate the limit: 1x + 9 lim x 9 x² + 2x - 63

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Q: Convert the following equation for a hyperbola into standard form, and graph it below using the…

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Q: Find 5 [(7x³ + 3x³) dz

A: use the algebraic property of integrals.

Q: Find the following limits. Show your work. x² + 3x lim a) x-4 x² - x - 12 lim b) x-0 tan(x) X

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Q: Given the vectors →u=⟨−3,2⟩ and →v=⟨−6,11⟩, find the angle (in degrees) between them. Angle between…

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Q: a) Find the radius and convergence of the following: xn Σ (n!)2 η=1

A: Given the series is ∑n=1∞xnn!2

Q: Use implicit differentiation to find the slope of the tangent line to the curve 3x³y + 7xy² = = 198…

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Q: 3) Show the the following derivative are equal. Then explain how they can be equal (don't just tell…

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Q: ∞ n=0 Find the radius and interval of convergence of the power series. Check the endpoints. (x-7)"…

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