Orthogonal Matrix Determine whether matrix A given below is an orthogonal matrix 0.8 0.6 00 -0.6 0.8 0 0 0 0 0.8 0.6 0 0 -0.6 0.8. A=

Q: Q4/ Find the directional derivative of the function F(x,y,z)=x+xcosz-ysinz+y at the point P.(2,-1,0)…

A: The given function is; F(x,y,z)=x+xcosz-ysinz+y

Q: 8x5 = 10 12 4 6. DeMarius' original design for his car used rear wheels with a radius of 12 inches.…

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Q: Define f(3) in a way that extends f(s) = f(3) = s³-27 s²-9 to be continuous at s = 3. (Type an…

A: We have to define f( 3) in a way that extends f(s) is continuous at s = 3.

Q: Evaluate the curvature of r(t) at the point t = 6. r(t) = (3- 7t, e³-18, 12t - t²) (Use symbolic…

A: The given curve is,Take derivative.Find its magnitude.

Q: Suppose the derivative of a function fis f'(x) = (x + 2)²(x-4)³(x − 6). On what interval is…

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Q: Find an equation of the plane passing through the points (1, -2,3), (4,5,-6), and (7,8, -3).

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Q: Use logarithmic differentiation to find the derivative of the function. y=(√x)** y'(x) =

A: Now we will find the derivative using logarithemic differentation.

Q: 1. What is the exact value of sin Answer: 12 ?

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Q: 0 00 Co o o o sin (²) = √³ انه ده

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Q: Let f(x)= = - [₁ f'(x) = f'(2) = todt. Evaluate the following.

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Q: Find the solution of the Euler equation on (0, ∞) with initial conditions x²y"-6y0, y(1) = 1, y(1) =…

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Q: Find the following for the vectors v= -4i + 7j -√√3k and u = 4i - 7j+√√3k. a. v•u, |v|, |u| b. the…

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Q: Find the area A enclosed by the curve r = 4 + sin(40)

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Q: Find the difference quotient of f; that is, find f(x) = 3x² - 4x + 2 f(x+h)-f(x) h h‡0, for the…

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Q: Question 1 Find the derivative of y=sin(3x² - 4x + 1). dy dx dy dx dy dx dx = - (6x-4) cos(3x² -…

A: The function is y=sin(3x2−4x+1)aim is to find the derivative of the given sin function

Q: s this function continuous at x=2? (Use three steps to justify all results) If it is discontinuous…

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Q: Evaluate 8x³16x² +5 x² - 2x 2 S dx.

A: formula used

Q: A volume is described as follows: The base is the region bounded by x = - y² + 6y + 117 and x = y² —…

A: from (1) and (2)

Q: [(x e²) x +e) ý = xe-3 − 1

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Q: The primitive of the function f(x)=x√√2+x² whose graph passes throu the point P=(√2,0) is: (a) =—=…

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Q: 5. (2) Evaluate the following limits at infinity. Justify your results. a) lim -3x7 +10x² 3x³-4x b)…

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Q: To illustrate the Mean Value Theorem with a specific function, let's consider f(x)=x²-x, a = 0, b =…

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Q: (1) Find the domain of the functions (a) f(x)=√2-5(x-1) (b) g(x) = log (10-x²-3x) by solving a…

A: The given function(a) (b)

Q: 3b b-2√4b+1-1 a) lim b) lim x-0 x²+16-4 x²

A: given limit

Q: Consider the curve parametrized by x = t¹ + 1 and y = tổ + 4t5. dy a) Find dx dy dx in terms of t.…

A: Here we will find dy/dx on doing differentiation of x and y with respect to t,

Q: Determine the interval(s) on which the following function is continuous. Then analyze the given…

A: f(x)=3ex1−e5x

Q: For r(t) = (3sint)i + (3cost)j + 4k Determine: 1. The unit tangent vector (T). 2. Principal unit…

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Q: James Stewart is the author of Calculus: Single Variable Calculus with Early Transcendentals (8th…

A: We need to explainIs Dr. Stewart right? Has Good triumphed over Evil? He would try to write out a…

Q: The point P(1, 1/5) lies on the curve y = x/(4 + x). If Q is the point (x, x/(4 + x)), use a…

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Q: Consider the parametric equations below. x = 1² y=t⁹ (a) Sketch the curve by using the parametric…

A: The given equation

Q: Find the volume of the solid generated when the region bounded by y = x³, y = 0, and x=3 is revolved…

A: The cylindrical shells formula for the volume of a solid generated by revolving a region bound by…

Q: Find the unit normal vector N to r(t) = (t, cos(t)) at t = 34. (Use symbolic notation and fractions…

A: Find the unit normal vector  to  at .

Q: The graph shows the depth of water W in a reservoir over a one-year period as a function of the…

A: To find the average rate of change of W between x = 0 and x = 150?

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

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Q: Classify each of the following ordinary differential equations by stating the order, determining if…

A: Order of differential equation: It is defined as the highest order derivative the differential…

Q: Find the directional derivative of the function at P in the direction of v. f(x, y, z) = xy + yz +…

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Q: (x-y)y’=x+y

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Q: Plot the point whose polar coordinates are -3, 6 options to change the snapping functionality of the…

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Q: Use the Squeeze Theorem to show that lim (x² cos 22x) = 0. Illustrate by graphing the functions f(x)…

A: given limit

Q: Hannah uses the substitution u = tan x and Akiva uses u = sec x to evaluate Stanxsec² xdx . Show…

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Q: 1 2 Let A = and let f(x) = 2x² - 4x + 5, g(x) x² + 2x + 1. Find f(A) and 4 -3 g(A). Remark. In the…

A: Given,.To calculate f(A) and g(A). This can be done as follows:

Q: In March 2014, a gas company had the rate schedule shown to

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Q: Find two positive angles and two negative angles that are coterminal with 610°

A: For finding the positive coterminal angle , add in the given angle For finding the negative…

Q: Find a cartesian equation for the curve r² = 4. Equation Use your answer above to graph r² = 4. Y 4…

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Q: A machinist is required to manufacture a circular metal disk with area 864 cm². Give your answers in…

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Q: Determine the intervals of continuity for the given function. At which endpoints of these intervals…

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Q: Maclaurin expansion of order 3 of the function f(x)= sinh(log (1-x)) is A) -x + 1 x ² - 1 x ³ + 0…

A: The given function is; f(x)=sinh(log(1-x)).

Q: Let C be the curve y = +16 15 14 13 12 11 10 9 18 4 3 = 8√x for 1 ≤ x ≤ 3.2. 1 Find the surface area…

A: Given that

Q: Consider the line passing through the points (2, -3,4) and (5,10, -12). Describe the line by a.…

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Q: Evaluate the limit analytically (without tables or graphs), using techniques that have been shown to…

A: The given limit is,