1. dt 15. y= 17. y 0 tan 0 d0

Q: L, f(x)dx + [° f(x)dx = 5. Si f(x)dx – Sº f(x)dx = 4.

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Q: Help Homer design a cylindrical silo to hold the output from his pet pig Harry Plopper. The silo…

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Q: xdy + (y – cos x)dx = 0, y (- = %3D

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Q: Find all relative extrema of the function. Use the Second-Derivative Test when applicable. (If an…

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Q: (d) Select the correct choice below and fill in the answer box within the choice. O A. lim f(x) = X…

A: Let's find.

Q: 6. Find the length of the curve r(t) = t'i – 2/2tj + (t – 1)k for 0 st<1. |

A: To find the arc length of the curve rt=t2 i-22t j+t2-1 k for 0≤t≤1.

Q: 6 + (-3) + 0 + ..+ 411 = 97 (a* + 5) - 0 k = 1

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Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the…

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Q: ||r(t) × r"(t)|| Use the formula k(t) : to find «(t). %3D r(t) = e"i+e-tj K(t):

A: K(t)=?

Q: A ferris wheel is 50 meters in diameter and boarded from a platform that is 5 meters above the…

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Q: Determine an equation for the tangent to the curve f(x) = 2x3 + 6x2 - 2  at x = -3

A: Given query is to find the equation of the tangent.

Q: Given h(r) = 1/r+3 find the following: (a)h(x2)= (b) h(x2 + 1)= (c)h(x2) + 1=

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Q: im Y cosx t Zx メナロ0 7x¢ し

A: Given query is to find the limit of the expression.

Q: Let ABCDEF is a regular hexagon with centre O. Let ā = 0A, b= OB and so on. Explain why/prove %3D…

A: We know that in an regular hexagon the distance from center to any vertex is same, then the…

Q: Evaluate the improper integral |. 3.x dx or show that it diverges. +1 x?

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Q: 5. Use the Second Fundamental Theorem of Calculus to find F'(x). х 1 F(x) = S* dt.

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise.…

A: Solution: ∯∂∂x6xy -∂∂y3xydxdy   (By green's theorem)

Q: Find the vector equation for the line of intersection of the planes x – 5y + 2z = 1 and æ + z = 1 |…

A: To find the vector equation of the line of intersection of given planes.

Q: (2) Prove that for any integer L () NTX / sin? dx = L. L -L

A: ∫ cos(ax) dx = 1a sin(ax) +C

Q: Evaluate the integral / (2x + 6y)dx + (15x – y)dy a C arc y = x² from (0,0) to (1, 1). NOTE: Enter…

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Q: Find the equation of the tangent plane to the graph of f(x, v) = In (17x² – 14y²) %3D at the point…

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Q: Solve the following differential equations of 1- yy' = 2y – x; r'y'y'+ xy' = 1 dy x + v

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Q: Use the first six non-zero terms of the Maclaurin series expansions for sin x and cos x to…

A: From the Maclaurin series expansion of sin x and cos x: sin x≈x-x33!+x55!-x77!+x99!-x1111!cos…

Q: Please help

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Q: d²s = 60/E – 18 subject to the conditions that ds = 5 and s= 11 when t= 1. Find the velocity v = dt…

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Q: CoS X F 2x 7x

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Q: Derive the Maclaurin series expansion for f(x) = COS x

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Q: Find the accumulated amount if AED 6,000 is deposited at 2.5% compounded semi-annually for 5 years.…

A: Given query is to find the amount accumulated.

Q: - In (e) - In7 Inlt 1. IN7(€ "-1) 2. In( e") 3.In(녹선) 4. In(글e) 1/-

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Q: r'y'y'+ xy' = 1

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Q: 11. Calculate the directional derivative of the function f(, y, z) = xyz at the point a (-1,0,2) in…

A: See the answer below

Q: Find the limit. NOTE: Enter the answer using round brackets. ) - () t2 + 8 1 lim tto \ 5t2 + 6'8t

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Q: Consider the solid of revolution obtained by revolving the region between the curves y=0 and y=x^2…

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Q: 20. Evaluate the limit lim 213

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Q: Approximate the point of intersection of the graphs of f and g. Then solve the equation f(x)=g(x)…

A: This question is related to Functions, we will solve it using given information.

Q: y = sin3x

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Q: Find curl (3z i + 4x j + 6y k). curl (3z i + 4x j + 6y k) = ( i )i + ( i )j + ( i )k

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Q: Find the volume of the solid bounded by the cylinder x2 + y2 =16 and the planes y=z, x=0, z=0 in the…

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Q: dy Solye the differential equation 3a2y = = -y, s.t. y (0) :

A: Topic = Differential equation

Q: Consider the parametric equations below. Assume that t can be any real number. x=t-3, y=2t-5…

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Q: Find the curvature and the radius of curvature at the stated point. r(t) = 7 cos(t)i + 3 sin(t)j+…

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Q: 21 The function f(x) is represented in the following table. Give the best estimate for f(x)dx 3 9.…

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Q: Determine the value of t that maximizes the area above the x-axis and below the graph of the…

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Q: Verify Green's Theorem by evaluating both integrals ам y? dx + x2 dy dA ay for the given path. C:…

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Q: Evaluate the line integral / -ydx + xdy along the curve C C : y? = 27x from (27, 27) to (0,0). NOTE:…

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Q: nd the S (1–) dx A. x– 2 In|x| – +c B. 3x – 2 In|x| –-÷+c C. 2x – In|x| –+c D. x– In|x| - +c

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) sin(9t), lim t-0 e5i +…

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Q: ,2 COS cos n Σ n3 n=1

A: Given problem:-

Q: Calculate D(fog) for the functions f(x, y, z) (st, tu, su).

A: answer is in next step

Q: Find V· (V x F), if F(x, y, z) = 7e"*i+ 9xe"j – 8e"²k. V· (V × F) =

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