Q3 :(A): By using "L' Hopital rules "; Find the limits of : (2) limx-o x-³ (tan-¹x - x)

Q: What is the distance between two points (3,-1) and (-2,-5). 3

A: Given that the two points (3,-1) and (-2,-5)  To find the distance between the two points.

Q: Calculate (9x10^7) divided by (45x10^3) show your work and answer in scientific notation

A: Given :   9×10745×103

Q: Q2: Solve the following integrals: (3) √ √dx dx (4) fxe* dx

A: The objective of the question is evaluate the indefinite integrals.

Q: (A): Solve the following linear equations by Cramer's rule: x + y + 2z=1 2x-y-z = 0 = 4 x +2y-z

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Q: Find an equation of the plane tangent to the following surface at the given points. zexy; (1,0,1)…

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Q: Use polar coordinates to find the limit. [Hint: Let x = r cos(8) and y = r sin(8), and note that (x,…

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Q: cos-¹ Q6A)If y cos = prove Zyy + z = 0. B) Z = (1 + i)(2-1)-¹, find |21. 倉

A: Simplify given equation in z then  two times partially differentiate z

Q: 10. √x(x² + 3x-8)dx A. -4 B. -404 105 D. -28 105

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Q: find the limit, if it exists. If the limit does not exist, explain why. limx→2 1−|x|^2/1−x^2

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Q: Suppose r' (t) = (cos(t), et, 2t) and r(0) = (1, 0, 3). Find r(t).

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Q: SULWAY 5. x- 7. dx 9. dt In Problems 7-16, obtain the general solution to the equation. dy -y-e³x =…

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Q: dw (C): If w = tanx and x = 4t³ + t ; Find dt dy

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Q: Find a differential operator that annihilates the given function. -2x+3x³+x²e5x

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Q: 08 06 04- 02 } } yex dxdy = y=0x=y² 0.2 04 06 08

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Q: 2 -1 -x²+8x-4 dx 1 x(x²+x-2)

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Q: You have decided to start saving for college and open up a 529 account. You invest $5,000 into the…

A: Given :Invest Amount=P=$5000Rate =r=2%=0.02Time =t=5 year

Q: (B): Find the tangent equation to the curve y = sin² x at point x F.

A: We can find the tangent equation at the given point as below.

Q: The volume of the solid obtained by rotating the region enclosed by y = x = 1, x = 7, y = 0

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Q: Compute u v if u and v are unit vectors and the angle between them is R|4

A: we know that u.v =uvcosθfor unit vector u=v=1given θ=π4

Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = 3 cos(t)i…

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Q: f(a+h)-f(a) h a. Use the definition mtan = lim h→0 b. Determine an equation of the tangent line at…

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Q: 12. (2xy³ + 1) dx + (3x²y²-y¹) dy = 0

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Q: Calculate the distance between the point Q(3, 1, 7) and the plane 2x - 6y – z = 3. Don't use a…

A: We need to calculate the distance between the point Q3,1,7 and the plane 2x-6y-z=3 without using the…

Q: Question 3 Given the U= {1,2,3,4,5,6,7,8,9,10) and A = {3,4,5,6,7} B = {1,5,7,9} C = {3,6,9} D =…

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Q: H.W: Evaluate the integral 30 [ (x²y - 2xy)dydx 0-2 1. 3. 5. 3 1 [ [(2x - 4y)dydx 2π π [[(sinx +…

A: 5.The given integral,        ∫π2π∫0πsinx+cosydx dy

Q: 3x 9. fxdx A.ln(e6x + 1) + c ₂-6x + c 3x c.exe Barctan (e6x) + c D.†arctan(e3x) + c

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Q: 11. f -dx 3x+1 +4x

A: these 2 questions are not related to each other so according to bartleby guidelines I need to solve…

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

A: To find v(t) ,s(t) and a(t) for the given position vector r(t).

Q: Let Vis the volume of the solid of revolution expressed by the equation V = 4n fx²e²dx. Find the…

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Q: (C): Solve the following equations:- (1) sin 2x + 2 sin² = 1

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 1. Solve the following a) 430.00(1+0.05) b) 1.2:4.2:60= 5 45 4 64 c) y: 9 8 (1+0.05)³3 -1 0.05

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Q: sin 8 cose √cos²0-9 c. f S do

A: Since, we have been asked to solve Part-C in which we have to evaluate the integral given…

Q: Compute the indefinite integral of the following function. r(t) = (13 cost,7 cos 5t,3 sin 6t)

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Q: Evaluate: x5 exdx when a and b are limits of integration such that a is the numerator and bis the…

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Q: what about part (b) please.

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Q: 3. 1 S [(2x - 4y)dydx 31 1 -1

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Q: Use the remainder theorem to evaluate the polynomial for the given values of x. g(x) =…

A: According to our guidelines, we can answer only one question or three subparts of a question. Other…

Q: Use polar coordinates to find the limit. [Hint: Let x = r cos(0) and y = r sin(0), and note that (x,…

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Q: 3) Consider the autonomous DE: y' = y² + 3y - 10 A) Find the critical points of the given DE.

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Q: 2 cy² = x² + y

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Q: dy Q5: Find for the following functions: (3) y = ex.sin² x In√x

A: We can solve this as follows:

Q: 2. 01 S -1-1 (x+y+1)dxdy

A: The Solution is given below

Q: The region is bounded by the graphs of the equations y = sin x, y = 0, x = 0, and x = π. dA = ( A =…

A: Here is your solution

Q: Evaluate the function at the given values of the independent variables. Simplify the results. f(x,…

A: Topic = Functions

Q: Compute the partial sums S2, S4, and S6 of 1 1 + 5.6 6.7 (Use symbolic notation and fractions where…

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Q: For what values of a and b is the line 2x + y = b tangent to the curve y = ax² when x = 4?

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Q: 3- If A² [45] [95] 091 (1 find A where A is UPF triangula matrix

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Q: Consider the following situation, which involves two options. Determine which option is less…

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Q: A pizza company is building a rectangular solid box to be able to deliver personal pan pizzas. The…

A: The given data is: A pizza company is building a rectangular solid box to be able to deliver…

Q: 2. Find the equation of the line tangent to the circle x² + y² + 6x - 2y - 15 = 0 at the point…

A: Here the given circle is , x2+y2+6x-2y-15=0 We need to find the tangent to this circle at the point…