For the points P₁(-5,3,4) and P2(4,5,0), find the direction of P₁ P2 and the midpoint of line segment P₁ P2.

Q: Calculate the arc length of y = 10x + 1 as a varies from 0 to 8. S =

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Q: Evaluate each limit (a) lim(x➡️b) (x³-b³)÷(x⁶-b⁶)

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Q: 285. 10 [(1 - cos ³0) e) cos²0 sinode

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Q: Consider the following. Function f(x)= arcsec(4x) Point (a) Find an equation of the tangent line to…

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Q: 1. If lul=lyl=2 and u+v+w=0, what is lwl? u, v, w are drawn below. u W

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Q: √16+h-√√16 h = (√16+h-√16) (√16+h+√16 h(√16+h+√16) 16+h-16 h (√16+h+ √16) h h(√16+h+√16) 1 Vh + 16 +…

A: To show :-

Q: 1. YA y=5r-r2 y=x (4,4) X

A: The given equation of curves are:.

Q: Given the equation x2 - 10x - 20y - 15 = 0. Write it in STANDARD FORM and find the following…

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Q: Problems 1-4, Find the average rate of change for each of the following graphs. Match the graph of…

A: A graph of the linear functions are given.The aim is to find the average rate of change of the…

Q: Q :- solve the following Bernoulli's equations. dy dx (2) + ytan x = y³ sec a 4 x

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Q: 9. For a general function y = f(x), what does - 10. If f(x) = x² + 3x + 2, find ƒ(5) - f(2) 5-2 ƒ(5)…

A: Given

Q: Evaluate the limit 4x + 9 lim x 11x²9x +9

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Q: A boat is pulled into a dock by means of a winch 12 feet above the deck of the boat. 12t 14 ft/sec…

A: Given:A boat is pulled into a dock by means of a winch 12 feet above the deck of the boat.Let x be…

Q: 3. Expand the following binomial functions by using given formula. n! [n-(k-1)][k-1]! finding kth…

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Q: 11. Expand the following binomial functions by using given formula. n! finding kth term of (a+b)"…

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Q: find a linear equation whose graph is the straight line with the given properties through (0.5,…

A: To find a linear equation whose graph is the straight line with the given properties: passing…

Q: 19. Let P denote the unit circle, parametrized in the usual way. Compute Jp F-dr, where F(x, y) =…

A: To compute

Q: Question Determine all intervals on which the graph of f is increasing. -6 -4 -3 -2 -1 -2 -3 -4 -6 1…

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Q: Sz/dx

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Q: Use the table to evaluate the limit of f (x). If the limit does not exist, use DNE. f(x) = limx→2…

A: From the table,as x approaches 2 from left side, f(x) = -1

Q: Find the area of the surface generated by revolving the curve x = 3 3 2' 0 sy≤4, about the y-axis.…

A: Styg

Q: Find the derivative of the function. f(t) = arccsc(-3t²) f'(t) = - 2 √√9-1

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Q: II. PARABOLA A. A parabola with the general form of the equation: y² - 4x + 6y - 11 = 0. Find the…

A: We have to find the standard form of equation, vertex, focus, latusrectum of the given equation of…

Q: Calculate the area under this function over the specified interval: f(x)=3x² +6x + 1; [-4,2] Show…

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Q: Compute the value of the improper integral. (If the integral diverges to ∞, type oo; if the integral…

A: The given integral is

Q: Find fx,fy, and f₂, and evaluate each at the given point. f(x, y, z) = x²y³ + 2xyz - 4yz, (-2, 1, 2)…

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Q: (6) Find the area of the region bounded by f(x) = x² – 2, g(x) = 6 – x²

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Q: what is the area of the parallelogram with the vertices : A=(0,0,1) B=(3,2,3) C=(5,3,5), D=(2,1,3)

A: Using cross product of vectors, we can find the area of parallelogram.

Q: Find the limit. (If an answer does not exist, enter DNE.) (x + Ax)² - 2(x + Ax) + 2 − (x² − 2x + 2)…

A: To find

Q: Use the given graph of the function ff to find the following limits. If a limit does not exist, type…

A: We have to find the limits using the given graph of the function.

Q: Answer the following True or False: Since lim then 1 8n + 2√√√n O True O False 1 n+∞ 8n+2√√n…

A: given limit

Q: In the figure, the equation of the solid parabola is y = x² - 7 and the equation of the dashed line…

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Q: A certain factory operates three different shifts. Over the last year, 200 accidents have occurred…

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Q: answer C and D of the same question. thanks

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Q: Let f(x) = lim f(x) = = x 6+ x f(6) = 3 x-9 Compute the quantities below. Write "DNE" if the limit…

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Q: Complete the table. y = f(g(x)) n(4x)) 9 y = sin U = u = g(x) y = f(u) y = sin(u)

A: Given

Q: Find the total differential. 5x + y 3z - 8y dw = W =

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Q: the functional F[y] = [[(y^)² - y² + 4ye™ ]dx such that y(0) = y(7/2) = 0. Calculate the minimal…

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Q: QUESTION 2 The graph below represents the distance-time relationship from Justin and Nicole as they…

A: To study the graph and answer accordingly.

Q: 14. Find a parametrization for the line segment in the plane going from (12, 42) to (7, 49).

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Q: Determine the sum of the following series. (3)"-1 8n n=1

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Q: For the curve defined by the parametric equations [x = 3 + sect y=3+5tant Find the first derivative:…

A: The given parametric equation of curve is

Q: 20. S2² In y dy

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Q: Determine if the function is even, odd, or neither. g(x) = 16x³1

A: Given:     g(x) = | 6x3 |

Q: -6 -5 -4 -3 -2 -1 9+ 8 7 6 AS 4 + The parametric curve defined by [x = 4tπ sin(2t) y=4-π cos(2t) is…

A: The given parametric curve equation is

Q: Evaluate the following integral using trigonometric substitution. x2 √√4+x² S =dx

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Q: A Beginning with the graph of y=sinx, use shifting and scaling transformations to sketch the graph…

A: In this question, we will draw the graph of the trigonometry functions.

Q: Suppose that the distance an aircraft travels along a runway before takeoff is given by…

A: GivenThe aircraft will become airborne when its speed reaches 400 km/h.The aircraft will become…

Q: Show that f and g are inverse functions analytically and graphically. - 1 f(x) = 5x + 1, g(x) = ) =…

A: f(x) and g(x) are inverse of each otheriff(g(x)) = g(f(x)) = x

Q: Let f (x)= - Complete the table below. Round all table values to four decimal places, if necessary.…

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