Calculate the velocity and acceleration vectors, and speed for r(t) = (sin(t), cos(3t), cos(t)) when t = 4. 4pi 4pi Velocity: "

Q: 1+x+y dzdyax Jc JO Jo

A: To evaluate the given iterated integral.

Q: B) Find the limits by using L.Hopital rule : 7x 1. lim x-0 sin 2x x2-16 2. lim X4 (Vx+5)-3

A: Using l hospital rule.

Q: Calculate y" and y". 4х — 7 y(x) %3D (Use symbolic notation and fractions where needed.) y" (x) =…

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Q: Using shell method, find the volume generated by revolving the area bounded by y = 2x – x2 ; y = 0 ;…

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Q: c). Find the area under the curve f(x) = 4x +2x over the interval (5,8)

A: Given,            fx=4x3+2x , the interval is 5,8To find : Find the area under the curve over the…

Q: A Moving to another question will save this response. tion 7 /2 Given f(x) = sin(x2) on [0, n/2],…

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Q: Determine if the geometric series converges or diverges. If it converges, find its sum. 3 4 4 +…

A: The series is of the form∑n=0∞45nsince 45<1 By geometric test ∑n=0∞45n  converges

Q: Select the conic section represented by the equation. y 2 = 3x line ellipse hyperbola circle point…

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Q: The discontinuities of the function f(x) = %3D 4х-9 are: х2—2х-15 Select one: O 5,3 O -5, -3 -5,3 O…

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Q: Estimate cos E- 0.1) + cos

A: Follow the procedure given below.

Q: Question 8 dx Evaluate the integral improper integral (2x – 1) 3 00 (А) 1/9 в) 1/6 (c) 1/8 D 1/4

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Q: Using "Numerical Differentiation (Forward Finite Difference)" Problem Solving f(x) = 2sinx - x3ex…

A: Given that the function is fx=2sinx-x3ex with h=0.002. It is required to find f'2 and f''2. The…

Q: Use the derivative f’(x)=x^2(x-5)(x+5) to determine The local maxima and minimal of f and the…

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Q: To find the distance across a small lake, a surveyor has taken the measurements shown. Find the…

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Q: Q1 Using a method of reduction to separable equation and reduction to linear equation, find the…

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Q: B) Find the limits by using L.Hopital rule : 7x 1. lim x-0 sin 2x х2-16 2. lim x-4 (Vx+5)-3

A: Given; (1). limx→07xsin2x

Q: Q2) Find the integral value for the following functions 3x 1. S 2. S(sec(4x) – 1)² dx 3. S dx V1+3x2…

A: The integration of the integrals is  1) 3x/sqrt(1+3x2) 2) [sec(4x)-1]2 3)1/[1+(5x+1)2]

Q: Sketch the region enclosed by y = 4x and y 4x. Find the area of the region. %3D %3D

A: Region÷

Q: 2. a) Determine the coordinates of all point(s) on the graph of y = 2x In x where the tangent line…

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Q: Given that i = and i = and that i • v = 188 determine the value of the constant A.

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Q: Current Attempt in Progress Consider the curve y = 6x3. The sketch of the portion of this curve…

A: Solve the following

Q: Q4) Find for the following functions (- dx Зх +4 %3D 2x+3 6. y = tan-1 V4x3 - 3 %3D

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Q: Calculate the following derivative if h(w) = Vwe3w. (Use symbolic notation and fractions where…

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Q: Find the exact arc length of the curve over the stated interval. y = 3r/2 – 4, from a = 0 to a = 1…

A: This question can be solved using the formula of arc length.

Q: 439) Use the matrix capabilities of a graphing utility to solvecif possible) the systems of linedr…

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Q: fx)-fla) Use the alternate definition, lim to determine the instantaneous rate of X- a 著→ 2 1 change…

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Q: The discontinuities of the function f(x) =D 4x-9 are: x²-2x-15 Select one: O 5,3 -5, -3 -5,3 O 5,-3

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Q: Q2/ Solve the Higher order differential Equations. (. d*y 16y = 0 2-

A: Here we have to solve higher order differential equation.

Q: Find fr(x, y) and fy(x, y) given f(x, y) = tan x· cos os(x² – y?).

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Q: Find the sum A+B+C of the constants A,B and C appearing in the Taylor series expansion given below:…

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Q: Derivative of f(x) = sin(x) 2 For each x-value indicated, drag the purple dots up or down to…

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Q: Q3) A) If you have three functions: f(x) = x2 – x %3D | g(x) = 3x – 1 w(x) = x2 – 2 So, find gof (x)…

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Q: In 7 years Harry and Sally would like to have $20,000 for a down payment on a house. How much should…

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Q: A rectangular picnic area of 8000 m² is being constructed along the edge of a river. It will be…

A: Explanation of the answer is as follows

Q: Q1) A) Find the tangent equation for the function: f(x) = Vx2 + 5 at x=2 ? %3D

A: As we know that; The slope of tangent line to the given curve is equal to the derivative of the…

Q: 5. Fill in the blank: For x, y ER. Equality in the Triangle inequality is satisfied, i.e. Ix+yl =…

A: x+y=x+ysquare on both the sides;(x+y)2=(x+y)2 x2+2xy+y2 =x2 +2xy+y22xy=2xyxy=xyis true only…

Q: Answer the following True or False. If | (f(=) - 9())dx D. gives the area betvween u – f(r) and 1 -

A: Inverse function means it is the reflection along the line y=x. Reflection does not change the area…

Q: If possible, find AB. (If not possible, enter IMPOSSIBLE.) 0 1 0 B = 3 1 A = -5 5 0 4 2 1 8 6 -1 7…

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Q: Jan paid Php 9,250 on a loan made 6 months before at 12% simple interest. Find the interest…

A: Amount Paid after 6 months= 9250 rate of interest=12%=0.12 Recall: Amount after time t years…

Q: To find the distance across a small lake, a surveyor has taken the measurements shown. Find the…

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Q: Find the total area of the region enclosed by y=x^2 and y=2x by integrating with respect to y. A…

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Q: Obtain the value of P3 (x) using Rodrigues' formula d" P,(x) = (x² – 1)" (2")n! dx"

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Q: Use the method of Lagrange multipliers to find the dimensions of the rectangle of greatest area x?…

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Q: Match the vector field with its graph. F(x, y) = yi 5 -5+ 5 5 5 |信

A: Given data÷ Fx,y=yi We need to find graph of function ÷

Q: 1(10,15) 2. An ant farm population is growing at a rate of g()=15e and declining at a rate of…

A: The rate of growth of an ant farm is gt=15e5t and  the rate of decline of the ant farm is dt=15e5t.

Q: ||F(t) × r"(t)|| ||r(t)||* Use the formula k(t) to find k(t). r(t) = t’i+ t®j K(t) =

A: See the answer below

Q: Here is a related rates problem: All edges of a cube are expanding at a rate of 5 cm/sec. Let the…

A: We have to choose correct options

Q: A. Solve the following problems using the concepts of Parametric Equations. Show complete solutions.…

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Q: Find all the values of t where the tangent line to the parametric curve is horizontal or vertical.…

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Q: QUESTION 10 Let D (x) = - 5x +7 and S(x) = 3x+ 1. Find the equilibrium point. 3.25 (-5, 32) (3, -8)…

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