4. Find the cosine of the angle between the normal vectors to the planes x+y + 2z = 3 and 2x -y + 2z = 5

Q: Find T, N, and K for the plane curve r(t)=(8cost+8t sin t)i + (8sin t-8t cos t)j, t> 0.

A: You have asked multiple question, we will solve the first question for you. The rest can be asked as…

Q: Given that 1. lim[f(x) + 3g(x)] = 2. lim[ƒ(x)]² x find the following limits. If a limit does not…

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Q: h (x, y) = 2xy + 3x² + 4x³y² +8 What is the value of Əh(x,y) dx when x = 3.8 and y = 1.5?

A: we need to find out the partial derivative.

Q: Preview Activity 10.4.1 Let f(x, y) = 6-2-², and let (To, yo) = (1,1). a. Evaluate f(x, y) = 6-2-y²…

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Q: Find the angle between the planes 8x + 3y = 4 and 10x + 5y + 6z = 10. The radian measure of the…

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Q: Suppose P(t) is the US population in millions today and t is in years. Match each statement (I)-(IV)…

A: Topic - Functions We are given P(t) is the US population in millions today and t is in years.

Q: Consider the following. Find the following partial derivatives. az as az at дz ди Find az Əs дz at…

A: Consider the following. z=x4+x2y, x=s+2t-u, y=stu2To find the partial derivatievs ∂z∂s, ∂z∂t,…

Q: Given that lim f(x) = 10, lim g(x) = 8, lim h(x) = 10, find the following limits x→a x→a x→a Enter I…

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Q: Find the domain of the vector-valued function. (Enter your answer using interval notation.) r(t) =…

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Q: If f(x) = f'(x) = 4 x³ t² dt then

A: we need to find the derivative of f(x).

Q: Find the area of the region bounded by the graphs of the function.f(x) = . Round your answer to…

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

Q: 5. Graph the function f(x) = log(x + 2) + 1. Identify the domain, the range, and the equation of the…

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Q: Find the area of the surface generated by revolving the curve about they-axis. y=81-x²,05x59

A: Given :y=81-x20≤x≤9about y-axis

Q: Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.…

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Q: Step 1 of 4: Find lim f(x). x-4- AV 10 5 Enable Zoom/Pan X

A: NOTE: Refresh your page if you can't see any equations. .

Q: An object is moving with velocity (in ft/sec) v(t) = t² — 2t – 8. Find the displacement and total…

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Q: Use the given graph of the function f to find the following limits: 1. lim f(x) = 5 x 17 2. lim…

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Q: lim. 3cosx x—> infinity

A: Explanation of the answer is as follows

Q: Given the points (-2,-4) and (-4, 2), find the rate of change between the points. Answer = (Round to…

A: Given :Points : -2, -4  and  -4, 2

Q: Given that f(x) = 9x - 8 and g(x) = 6 - x², calculate (a) f(g(0))= (b) g(f(0))=

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Q: Explain why the function is discontinuous at the given number a. (Select all that apply.) F(x) = if…

A: We have to find the limit and graph the function.

Q: Use the integration capabilities of a graphing utility to approximate the arc length of the graph…

A: Using integral

Q: f(x) = log(x) + log₂ (x)

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Q: Let R be the region bounded by the following curves. Find the volume of the solid generated when R…

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Q: te the following: 2x dx x - 4 dx

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Q: Consider the equation below. 16x² + y² + 16z² - 8y - 160z + 400 = 0 Reduce the equation to one of…

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Q: Given that lim f(x): x→a (a) lim[f(x) + 6g(x)] x→a (b) lim[f(x)g(x)] x-a Enter I for ∞, -I for -∞,…

A: Since you have asked multiple part question, we will solve the first 3 parts of the  question for…

Q: 3. Determine the following function f has a removable discontinuity at c. Rdefine f(c) so that f is…

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Q: It costs Charlie $14 to build a certain birdhouse. He estimates that, if he charges x dollars per…

A: It costs Charlie $14 to build a certain birdhouse. He estimates that, if he charges  x dollars per…

Q: Let F be the function whose graph is shown below. Evaluate each of the following expressions. (If a…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: Explain how each of the following features relates to a function's derivatives and curve sketching.…

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Q: The graph in the figure is a horizontal and/or a vertical shift of the graph of y=x^2. Find a…

A: Here we have to plot a graph.

Q: Find the limit. (If the limit is infinite, enter '∞o' or '-co', as appropriate. If the limit does…

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Q: Set up and evaluate the integral that gives the volume of the solid formed by revolving the x²…

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Q: Find f’(a) F(x)= 1/ sqrt (x+2)

A: Given: fx=1x+2 ⇒fx=x+2-12 To find : f'a

Q: the Cartesian equation xy = 21 with an equivalent polar equation. ivalent polar equation is…

A: Topic:- calculus

Q: The domain of the function is (80,∞) 3, g(t) = t - 80

A: Domain of g(t)= t-803

Q: a) Graph the function f(x)=x² + 4x. b) Draw the tangent lines to the graph at the points whose…

A: Correct option is D.

Q: The width of a rectangle is 15. Express the area A of the rectangle as a function of its perimeter…

A: Given width of rectangle =15 perimeter of the rectangle =PWe need to find the area in terms of P.

Q: Calculate an explicit general solution for the ODE: dy dx To get full credit, you must use the…

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Q: Let f(x) = 2x + 2 and g(x) = 4x² + 4x. After simplifying, (fog)(x) =

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Q: All of the functions below have a domain of all real numbers EXCEPT for one of them Which function…

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Q: Use the shell method to write and evaluate the definite integral that represents the volume of the…

A: Here is the integral .

Q: Solve x³ + 3x² - 4x=0. Enter the values below. Smallest value: x= 0 x Middlex value: x= 0 Largest x…

A: Given :x3+3x2-4x=0

Q: Given lim f(x) = 5 and lim g(x) = -1, evaluate: x-7 x-7 lim (g(x) In (4f(x) — 4)) = x-7 lim…

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Q: Evaluate d/dt(r1(t) · r2(t)) at t = 0, where r1(t) = ⟨−6,8t,e^t⟩, r2(0) = ⟨1,6,2⟩, and r′ 2(0) =…

A: Given r1( t ) = { −6, 8t , et } r1'( t ) = { 0 , 8 , et } at t = 0 r1'( 0 ) = { 0 , 8 , 1 }

Q: (a) Evaluate: i) sin (b) Simplify the expression sin 7T ii) cos COS 5T cos(2 sin (3x)) + 3log (182²)…

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Q: If f(x) = ex+4, find and simplify f(1 + h) – f(1) . 0 e4 (eh - 1 ) 0 ch + h () es+ h 0 (0 - 1) کین 0…

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Q: 2. Which of the following function is continuous in R? Of(x)=√x² + 1 + 1 Og(x)=√x³ Oh(x)=√ Op(x) =…

A: INTRODUCTION Using the notion of continuity, one must check that the limit of the function at the…

Q: Given that f(x) = 2x − 2 and g(x) = 7 - x², calculate - (a) f(g(-3))= (b) g(f(-3))=

A: fx=2x-2, gx=7-x2, fg-3