Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(1) = i – 26j + %3D (a) r(t) 3ti- 2j + 2 k (b) r"(t) 31 + 5kt (c) r'(t) · r"(t) 257 + 18. (d) r'(t) x r"(t) 15 -10ti

Q: Find the indefinite integral. (Use c for the constant of integration.) (4t3i + 14tj – 6/tk) dt

A: we have to find the indefinite integral

Q: y" - 2у/ + у 3 tet + 4, y(0) — 1, у (0) — 1 || %3D

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Q: I. Find the derivatives of the following 1. f(x) = 2x2 + 3x - 7 %3D

A: We know that ddxxn = nxn-1               and                    ddxpxn = p ddxxn = p× nxn-1 = pnxn-1

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Q: 2) Find and of the following equation then simplify whenever possible. d²y dx dx² x = Cos ß + Sin ß…

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Q: Using the Nth term test for divergence 5 1 n=1_2n +14 5 diverges since lim is equal to 1 2n+14 O 1/3…

A: We can answer the question as below.

Q: (3x? + у?)dx — 2хydy %3D 0

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Q: Evaluate the integral of (3x2 + 9y2) dx dy if the interior limits has an upper limit of y and a…

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Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by…

A: Given: x=4y, x=-4y, y=1   From the given curves the bounded region is as shown below;

Q: y" + 9y = 9 sec² 3t, 0<t < T/6

A: To solve the following differential equation

Q: Take

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Q: Consider xy2+x2y=6, find the slope of the tangent line at the point (1, 2)

A: Given query is to find slope of the tangent at given point.

Q: Evaluate the line integral -ydx + xdy along the curve C: y? = Зх from (3,3) to (0,0). NOTE: Enter…

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Q: The position vector r describes the path of an object moving in space. Find the velocity v(t), speed…

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Q: 5. J 12 csc (-6х) cot (-6x) dx 6. J2x3 cot х4 dx 7. S xª sec (x5 - 9) dx 8. S tan 3 x dx

A: The given integral are 5) 12 csc(-6x) cot(-6x)  6) 2x3 cot(x4)

Q: Find the magnitude of the given vector. (-3, 6, 2)

A: Given,            The vector is &lt;-3,6,2&gt;.To find : The magnitude of the given vector.We know…

Q: Which integral corresponds to the volume of the solid generated by revolving the region enclosed by…

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Q: 1. Find the area of parabola y = x² from 0 to 1.

A: This is a problem related to integration. Based on the integral formula for area calculating we will…

Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

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Q: Find the area of the region bounded by  y=x^3,y=x+6 and       2y+2=0.

A: This is a problem related to integration. Based on the general formula and concepts we will answer…

Q: For the given cost function C(1) = 128/a + find 512000 a) The cost at the production level 1800 b)…

A: "According to the guidelines issued by the company we are supposed to answer only first three…

Q: A = (0, -3) and B = (5,9) A = (3, – 11) and B = (9,-3)

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Q: 7. Sketch the region of integration, and evaluate the integral. 2 2x. JI zdz de dr .2

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Q: Since log,(a) = c → a = b°, 1--2 In(즉)- e-1/2. » X = So, y' = 4x(1 + 2 In = 0 when x = -1/2 and y" =…

A: Since logba=c→a=bc                          1=-2lnx5  ⇒-12=lnx5  ⇒e-12=x5⇒5e-12=x⇒        x=5e-12

Q: function f has the following graph: 4- 3 2 1. -1 6 7. 8 -1 -2 Vhich of the following is true? O The…

A: Given query is to find the correct statement for the function.

Q: Find the area of the plane region bounded by y = x - 4x and y% x(2-x). Answer

A: As per Bartley guidelines we are supposed to answer only one question per post.  This post contains…

Q: 4.) on this item Pinal (Vx+Vx)* dx Use only The Method of substitution/u-substitution answer should…

A: We have to find the integral

Q: L 3x2 dx = 65 %3D Select one: O True O False 2Vadx = 104/3 Select one: O True O False L (x +4)(2 +3)…

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Q: 6. sin x (1 + sin x cos x) dx y csc² ( tan (y²)) dy 7. cos²(y²) sec (11w) tan (11w) V (2 – sec…

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Q: A local pond can only hold up to 51 geese. Seven geese are introduced into the pond. Assume that the…

A: This is a problem related to differential equation and exponential function. Based on the general…

Q: EVALUATE EACH OF THE FOLLOWING INDEFINITE INTEGRALS. Show step by step solution. dx

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Q: Since y"|? v0 at x = -1/2 e we have a relative minimum at the point (c, f(c)). Substitute c = 5e¬1/2…

A: Solve it

Q: e2y dy Solve using algebraic substitution Tey-i

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Q: Solve the exponential equation algebraically. Approximate the result to three decimal places. (Enter…

A: We have to solve above algebraically solution

Q: integral

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Q: Using appropriate substitution | sec*x dx is equal to In|secx + tan x| -1 + C 2cos?x + sec x tan x +…

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Q: Find the curvature and the radius of curvature at the stated point. r(t) = 10 cos(t)i + 11 sin(t)j +…

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Q: Ow dw Find dx' dy and dz using implicit differentiation. Leave your answers in terms of x, y, z, and…

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Q: Determine whether the series converges or diverges. Make sure to clearly state the test that you're…

A: Given,  ∑n=0∞2xnn!

Q: A population of 200 kangaroo is released into the forest. During the first three years, the…

A: Given,initial kangaroo number, n(0) = 200number of kangaroo after 3 years, n(3) =500carrying…

Q: t cos t?dt can best be evaluated by: A None B Trigonometric Transformation Integration by Parts…

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Q: (x² + 1)3 y = (x3 – 1)

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Q: dy Find for dx 5) y = sec-(2e3x)

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Q: An arithmetic sequence has first term a = 5 and common difference d = 8. How many terms of this…

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Q: b. S 2*³-4x²-x-3 dx х2-2х-3

A: First we divide the polynomial  using long division

Q: Find the partial derivatives of f(x, y) = 5x*y². %3D

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Q: 2. y = x5 + 2x* + 5x3 + 4x² + x +1

A: Find the derivatives by applying basic differentiation rules.

Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

A: Follow the procedure given below.

Q: If the function f(x) is continuous in the interval [-7.0] and f(-7) = 32 and f (0) = –1, then which…

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