D Question 11 Find the slope of the tangent line to the curve y=rarcsin z at the point 02 √3 01/ O O 7/3 2' 12

Q: Find the specified nth term in the expansion of the binomial. (x + 2z)?, n = 6

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Q: (8z i + 9x j + 2y k) = (i k )i + ( i )j + (

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

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Q: Use sigma notation to write the sum. 1 7 (2) + 7 (3) j = 1 1 7(1) + 1 7(10)

A: The given sum 171+172+173+.....+1710

Q: Use the Binomial Theorem to write the expansion of the expression. (2√t-3)³

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Q: Find the unit tangent vector to the curve at the specified value of the parameter. (₁)-[ = T T r(t)…

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Q: Determine whether f is continuous, piecewise continuous, or neither on the interval 0 ≤ t ≤ 3. 31²,…

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Q: Verify the identity. (Simplify at each step.) Let 8 = sin X-2 tan(sin−¹(*²)) = √9+ (x - 2)² X-2 -¹…

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Q: For the function, do the following. f(x)=√x from a = 2 to b = 5. (a) Approximate the area under the…

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Q: 1 Find the linearization of the function f(x) = 5x+4 atz-1.

A: The given function fx=15x+4 at x=-1

Q: - A gardener has 120 feet of fencing to fence in a rectangular garden. He wants one side of his…

A: According to the question: l+3w=120 or l=120-3w a)The area A of the garden is:           A=lw…

Q: (Question #1, 2, 3, 4, f(x)=x²e* f(x) = et'nx f(x) = ln(4x³ + x) 1. 2. 3. ror the following…

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Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

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Q: Problem 4.10 Find the slant asymptote of and sketch the curve. y = 2x³5x² + 3x x2 -x-2

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Q: A manufacturer can produce 5130 cell phones when a dollars is spent on labor and y dollars is spent…

A: Topic- Implicit differentiation

Q: Find the gradient of the function w = 2x²y - 4yz + z² at the point (1, 1, -2). ○ 2î+ 10j - sk Ⓒ41+…

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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: Find the third, fourth, and fifth partial sums of the series. Σ(3) j = 1 (a) third partial sum (b)…

A: The given series is ∑i=1∞12i

Q: Consider the function f(x) = 8x³ - 2x² + 3x - 6. An antiderivative of f(x) is F(x) = Ax¹ + Bx³ + Cr²…

A: Integrate both side in equation and comparison to given equation

Q: For the function f(x,y)=−5x2+2xy+3y2−x−5y+1f(x,y)=-5x2+2xy+3y2-x-5y+1, find a unit tangent vector to…

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Q: all explain the range and domain for each. (6) Draw the graph of the function f(x) = (7) Graph the…

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Q: Q13) S 3+eZx dx

A: we can solve this as follows:

Q: { h=1 (05/30) n+42

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Q: Find div F and curl F if F(x, y, z) = 16yªz³i – 17x7zºj − 3xy¹k. div F= curl F=

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Q: Two cars are moving towards an intersection. One car is 150 meters north of the intersection and…

A: This is a problem related to distance and velocity. Please find the procedure given below.

Q: Use Theorem 7.1.1 to find (ft)). (Write your answer as a function of s.) f(t) = (et-e-t)² L{F(t))

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Q: Find the AREA of the region bounded by: y = √√√x+2, y=x, and the x A. B. C. D. 37 6 19 6 10 3 16 3 F…

A: Topic = Area

Q: Find the slope of the tangent line to the curve - 3x² – 3xy - 4y³ = 265 at the point (1,4).

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Q: Question 4 Find the gradient of the function at the given point. w = 2x - 4yz+z², (1, 1, −2) 21+…

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Q: Locate all relative maxíma, relative miníma, and saddle points, if any. f(x,y) = 8x² + xy - 3y - 6x…

A: Given function, f(x,y)=8x2+xy-3y-6x+2.

Q: Use the definition of the Laplace transform to find L{f(t)}. (Enter your answer in terms of s.)…

A: laplace transform

Q: Question 14 A line is tangent to y = x³ - 2 at (2,6). What is the coefficient of x when the line is…

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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: Evaluate: 00 O 2 12 3 O dne O 2√14 7 lim, 47 16-2 12+x-r²

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Q: Please answer and write correctly and neatly. Given the vector field Ā= 2x2y ax – 2(z-x) ay + 3xyz…

A: Solution is given below:

Q: Write the first five terms of the sequence defined recursively. a₁ = 5, ak+1 = 4(a-3) ak+1 a₁ az 33…

A: We will find the required.

Q: Solve the equation on the interval 0 ≤0<2 cos (30)=1 MAN What are the solutions to cos (30) = 1 in…

A: Solve the trigonometry equation

Q: Write the first five terms of the arithmetic sequence defined recu = 2.5, a 0+1=3 +0.75 (0 82 N 33…

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Q: A manufacturer can produce 2700 cell phones when a dollars is spent on labor and y dollars is spent…

A: Given problem:- A manufacturer can produce 2700 cell phones when a dollars is spent on labor and y…

Q: Evaluate if possible 1 [₁²x5+¹ dx -2 x3 ….…..

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Q: Find the Laplace transform Y(s) = L{y} of the solution of the given initial value problem. Y(s) = y"…

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Q: The following figure gives the graph of the derivative of a continuous function f that passes…

A: answer is in next step .

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

A: We know that for a position vector  rt = xt, yt, zt, velocity  vt = r't = x't, y't, z't speed  st =…

Q: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method,…

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Q: The marginal average cost of producing x digital sports watches is given by the function C'(x),…

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Q: Find a differential equation whose general solution is y = C₁e6t + c₂e-4t y" - 2 y' - 24 = 0 X

A: The solution of the DE is: y=c1e6t+c2e-4t where the solutions to the auxiliary equation are 6 &amp;…

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

A: As per our guidelines we only solve one question and rest of the question will be reposted.

Q: Find the nth Taylor polynomial for the function, centered at c. P4(x) = f(x) = 1 +2, n = 4, c = 5

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

A: O

Q: The inverse forms of the results in Problem 49 in Exercises 7.1 are 2² (6-³) and s-a y(t) (sa)² +…

A: Given :y'+y=e-6tcos5ty0=0L-1s-as-a2+b2=eatcosbt and L-1bs-a2+b2=eatsinbt