Consider the indefinite integral 14 This can be transformed into a basic integral by letting du and du +6 dz dz: Performing the substitution yields the integral

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Q: Find T(t) and N(t) at the given point. r(t) = 2 cos(t)i+2 sin(t)j; t = (7) 3 T N ㅠ = = 3

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Q: Provide a set of parametric equations for the function f(x) = x² sec² (2x + 1).

A: We are given a function we need to find the parametric equations for the given function.

Q: can you do it one more time to double check pls

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Q: Write the function f(x) = √1 + x² as a polar function.

A: Let

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Q: The Map As you walk through Gate 4, you realize that Gate 5 is nowhere to be found. In front of you…

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Q: 2. If = (a, b, 1) is perpendicular to both = (5, 1,-2) and w = (3,-3, 6), find a and b.

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Q: (a) In(28) - In(56) is equal to In(4) - In(8). OTrue OFalse (b) In(a + b) = In(a)In(b) for all a,b >…

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Q: Let y = Ա 4 + DIS 5 Ա and u = x³ = x³ - 2x.

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Q: (a) [ƒ(x) + 9(x)]| d dx d (b) f(g(x))] dx d dx (c) · |[(x)6 · (x)ƒ]² x=1 d [g(x) (0) dx f(x) x=1…

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Q: Find the following limits: a. lim 1200 e t→∞ -0.2t= b. lim 1800 + 1200 e¯0.2t = t→∞ 400 t∞ 1 + 3 e…

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Q: An investment appreciates 2% per year. Originally $5000 is invested. After how many years to one…

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Q: How many critical points does the function f(z) - 6sin² (52) have on the interval (0,)? Provide the…

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Q: Sketch the graphs of the functions f and g. f(x) = e, g(x)= O -10 -10 -5 -5 - y 10- y 5 101 5 -10- X…

A: Using integration, we can find the required area.NoteAccording to our guidelines, we can answer only…

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Q: Since YouTube first became available to the public in mid-2005, the rate at which video has been…

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Q: Find the linearization L(x,y,z) of the function f(x,y,z) = √x² + y²+z² at the points (7,0,0),…

A: To find the linearization  of the function  at the points , and .

Q: Show diagram, define variables, state formula, theorem, equation or function used, Show…

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Q: find the sum of 27+54+81+108+...+540

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Q: 1. Given the diagram below, determine the angle made by the diagonals AD and BC.

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Q: Determine the equations of the asymptotes for the hyperbola: +5²_ (x + 2)² =1 9 =-=-*- , y = x = -2;…

A: The given equation of hyperbola is; (y + 5)2/4 - (x+ 2)2/9 = 1Find the asymptotes.

Q: Use Green's Theorem to evaluate: F.ñ ds where F =(√x+3y, 2x + 3y) and C is the boundary of the…

A: The solution is shown in step-2

Q: Use cylindrical coordinates to calculate the triple integral [ f(x, y, z) dV for the function f(x,…

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Q: A child runs 50 m from a slide on a playground to a lemonade stand which is on a bearing of 120°.…

A: Bearing of lemonade = 120°Bearing of ice cream stand = 170°Length b/w slide and lemonade stand =…

Q: 6-Use the algorithm for curve sketching to sketch the following:( Show all steps) Y = -10x³ + 3x² +…

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Q: f(x) = 5xe² -2 -2 -1 -2 1 Find the area of the region bounded by the graph of the function f and the…

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Q: 7- Determine the absolute and local extreme of each function on the given interval. a) f(x) =…

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Q: Find the indicated derivative. If y = x6x¹/2, find d²y dx² d²y dx²

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Q: We have In (10-x) = C-1 Σ 10 n=0 +7+1 10^(n + 1) =C- In order to find C, we let x = 0 and get f(0) -…

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Q: Find the arc length of the graph of r(t) = e√²ti + e-√²tj + 2tk, 0≤ t ≤ √2ln6 NOTE: Enter the exact…

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Q: evaluate the following 3 Sim хусо х X b) lim e^ е X7-00 C) Sim x3 X700 3x+1

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Q: Find the volume of the largest rectangular box in the first octant with three faces in the…

A: Find the volume of the largest rectangular box in the first octant with three faces in the…

Q: Use Green's Theorem to evaluate the line integral. J 2xy dx + (x + y) dy C: boundary of the region…

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Q: f(x)=ln(x+1) Find the inflection points.

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Q: If csc(x) = 2, for 90° < x < 180°, then () = [ 2 sin ()=0 2 tan (5) = [ COS

A: Csc(x)=2, 90&lt;x&lt;180Find sin(x/2)Cos(x/2)tan(x/2)

Q: The Fifth Gate After traversing your continuous path, you finally arrive at Gate 5. Your computer…

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Q: What transformations must be applied to y-log(x) in order to generate y=2log(x)/log(0.5) O O O O 1.…

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Q: Substitute the value of y' in 1 + (y)²

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Q: Find the function f given that the slope of the tangent line to the graph of f at any point (x,…

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Q: The Equations for the asymptotes for a hyperbola with a vertical transverse axis are given by:…

A: asymptotes of the hyperbola with a vertical transverse axis.

Q: For the following exercises, refer to the figure of baseball diamond, which has sides of 90 ft. 3rd…

A: Note : As per our guidelines we are supposed to solve only one question. Kindly post second question…

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Q: 10 0 1 y = ex 3 X

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Q: 1. Ema thinks that (i) x w, exists. Paul disagrees with her. Who is right? Explain why.

A: The dot product results in a scalar quantity, while the cross product results in a vector quantity.

Q: Find the slope of the tangent line to the parametric curve r(t) = cos 2t and y(t) = sin(-t) at t =…

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Q: 5. A toy manufacturer figures that it costs $4 to make a toy car. There are fixed costs of $500 per…

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Q: Find the value(s) of t so that the tangent line to the given curve contains the given point. r(t)…

A: Using concept of derivatives and tangent line, we can solve the question.